solve each inequality and graph its solution answer key

b. b. All problems have only positive, whole numbers. On the left side, draw 3 negative rectangles to model -3x and 6 positive squares to represent 6. c. -6 Explanation: We are given that the rate of change is -4°C per hour so the final temperature is -4 times the number of hours. Subtract 12 on both sides The original price is $42 so the discount price is 42 – 3x 14 – 11 < k + 11 – 11 Since the inequality is ≥, we use a closed dot and shade the line going to the right. 3 + x < 7 Add 2.5 on both sides m = -11 Thus the correct answer is option B. c < -40 Write a two-step inequality you can solve to find h. Answer: Since the two inequalities are joined by “and”, we need to satisfy both inequalities. $\frac{b}{9}$ − 34 + 34 < −36 + 34 Question 6. __________. Type below: Question 1. While this is not a complete check, it often helps verify the solution. Thus the correct answer is option C. Question 8. In golf, the lower your score, the better. How much change did she get back? Its graph would like the one below: Question 13. Multiply the price per pound of potatoes by the number of pounds. Gary has enough money to buy at most 5.5 pounds of potatoes. Compare the two methods. Write a situation for 15x − 20 ≤ 130 and solve. Shawnee solved the inequality using the algebraic method you used in this lesson. (−0.5x − 4) − 1.5x – 2.3 h ≤ -2, Question 1. We need to use the fact that the final temperature is equal to the rate of change in temperature times the number of hours. b. The math tutor charges $30 initially but has a constant rate of $25 per hour after. Explanation: ___________. Choose a value in each section and substitute it in the original inequality to see if it makes the inequality true or not. __________. Ex: 4.7-2-Create your own worksheets like this one with Infinite Algebra 2. Type below: h < 10 y = 30 + 25(4) y í 8 < í3 or y + 5 > 19 $16:(5 y < 5 or y > 14 í11 2h í 5 13 $16:(5 í h 3z í 2 > í5 and 7 z + 4 < í17 $16:(5 Define a variable, write an inequality, and solve the problem. The number of hours that the physicist can change the temperature of the metal is then at most 20 hours. 8x + 16 From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. Use the above inequality, Answer: The solution set for x < 2 and x > 7 sould be (-∞, 2) ∪ (7, ∞). −25 + $\frac{t}{2}$ + 25 ≥ 50 + 25 6.5 − 4t – 6.5 ≥ 1.5 – 6.5 The inequality 80 − 2w ≥ 50 can be used to find w, the width of the rectangle in inches. Let t represent the temperature in degrees Celsius. Identify what your variable represents. d. 0.85x − 1.65 = 20. Its graph would like the one below: Question 17. Multiply the two fractions by first writing 4 $\frac{1}{2}$ as an improper fraction then cancel the 2s and then simplifying the division. Exercise 2 2 If the singer is ill, they'll cancel the. Type below: m = -12 n + 7 < −3 ___________, Explanation: The number opposite the variable is 4, we look for this in the number line. __________. 4x + 12 – 12 < 4 – 12 Thus the correct answer is option B. If the temperature must be no colder than -80°C, then the final temperature must be greater than or equal to -80. $\frac{9}{5}$C < -72 How many hours will it take to warm up the metal? Explanation: Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. d. 3x + 6 ≤ 3 Answer: 7x is the solution multiplied by 7. ___________. x ≥ 19.75, Question 21. The number opposite to the variable is 6, we look for this in the number line. Since there are 7 kittens, each kitten weights less than 3.5 ounces, and 7 × 3.5 = 24.5, then the combined weights of the kittens must be less than 24.5 ounces. ___________. x = 5.2 cm, Question 2. Question 26. ___________, Answer: Grace earns $7 for each car she washes. The vet says that Lena’s puppy will grow to be at most 28 inches tall. ___________, Explanation: If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Subtract 12 on both sides What inequality can you write to find the number of shirts he can buy? p ≥ -6, Question 3. a. Marie scored 95, 86, and 89 on three science tests. __________, Explanation: 3 + x < 7 p Worksheet by Kuta Software LLC Solve each compound inequality and graph its solution. $16:(5 true WRITING IN MATH Write a how -to manual for determining where to shade when graphing a system of inequalities. −12x < 60 All problems have only positive, whole numbers. 52 ≠ 68 ___________. Each group would then have 3 positive squares on the left side. Options: During a scuba dive, Lainey descended to a point 20 feet below the ocean surface. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Write an inequality to find the numbers of bagels Nick can buy. _______ people. z ≤ 64, Question 13. __________. $\frac{z}{4}$ ≤ 16 Write an equation for the cost c of h hours of tutoring for either service. Example 3 Graph the solution for the linear inequality 2x - y ≥ 4. 51 ≠ 45 Type below: c. 0.75n + 1.75 ≥ 20 30x + 600 ≥ 1,500 0.85x + 1.65 = 20 Answer: 0.5 ≤ $\frac{y}{8}$ Type below: 6.5 − 4t ≥ 1.5 ___________, Answer: __________, Explanation: ___________. d. 0.75n + 1.75 ≤ 20. p + 4 62/87,21 The solution set is { p | p ` n eSolutions Manual - Powered by Cognero Page 1 5-1 Solving Inequalities by Addition and Subtraction. -4b ≤ −16 Solve each system of inequalities by graphing. Explanation: (8)0.5 ≤ $\frac{y}{8}$(8) 39 + 8(6) = 39 + 48 = 87, Question 14. For how long can the physicist change the temperature? Answer: To graph inequalities, locate the number opposite the variable of the inequality on a number line. Answer: 5(12) – 8 = 68 Subtract 10 on both sides Which of the following is the solution set of !3 $ 2. x # 7 & 13? c. −4n + 11 < −9 y > 6 To graph inequalities, locate the number opposite the variable of the inequality on a number line. Answer: Type below: This leaves 9 positive squares on the right side. 27t + 36b, Question 4. b. $\frac{9}{5}$C + 32 – 32 < −40 – 32 __________, Explanation: Selena has $10. Question 9. Since the inequality is <, we use a hollow dot and shade the line going to the left. First, solve the inequality: ___________. Divide both sides by -5 The inequality is then -4t ≥ -80. Type below: Max wants to buy some shorts that are priced at $8 each. To graph inequalities, locate the number opposite the variable of the inequality on a number line. The third step is to determine what inequality sign to use by determining if you need to be greater than, greater than or equal to, less than, less than, or equal to the target amount to write the inequality. On this worksheet, students will find and graph solutions to basic, one-step single variable inequalities. k is no greater than 9 Answer: Both involve using the same operations. To graph inequalities, locate the number opposite the variable of the inequality on a number line. -20 + 18 > -4 Its reciprocal is the n bigger than 1, such as 1/$\frac{1}{4}$ = 4. The inequality is then -20 -20x ≥ -100. Write an inequality you could solve to find the number of minutes she can continue to descend if she does not want to reach a point more than 100 feet below the ocean surface. He bought lunch at school, paying $2.25 for each meal. 3 – 3 + x < 7 – 3 Show your work. d. 30x + 600 ≤ 1,500. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. The number opposite to the variable is -7, we look for this in the number line. −6w − 18 ≥ 36 Which graph models the solution of the inequality −6 ≤ −3x? Multiply 2/13 on both sides 55 > −7v + 6 For a graphical solution, treat each side of the inequality as a function and graph the two functions. 3x + 57 d. 5x −8 = 68 c. Describe the solution set of the compound inequality x < 2 and x > 7. -16 ≥ y Type below: 2s ≥ 44 She always saves $25 of her weekly earnings. The members have already raised $750. The number opposite to the variable is 8, we look for this in the number line. Type below: Show your work. If you want to score the highest marks in the exams you have to practice the problems a number of times. t ≤ 10 Write an inequality. By using this website, you agree to our Cookie Policy. Since you can’t buy a fraction of a pair of shorts the most pairs he can buy is 4. She paid with a $10 bill. Solve each inequality and select the answers that are in the solution set. You are going shopping to buy some shirts. 3 ≥ 0 true, Question 6. Answer: a. Solve each compound inequality. 2 ≤ 5, Question 2. ___________, Explanation: C. y â!2 or. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Divide both sides by -4 remember to switch the inequality sign since you are dividing by a negative number. For groups of up to 8 people, the cost per ticket decreases by $3 for each person in the group. This means the temperature will reach a temperature cooler than -80°C if he cools the metal for more than 20 hours. Type below: 2x < 16 d. 5x −8 = 68. Explain how inequality demonstrates that fact. Explanation: x = 4 Less Than Or Equal To Type <= for "less than or equal to". Analyze Relationships Type below: 5d − 13 < 32 Divide -7 on both sides x > 9 Explanation: Shed the societal and cultural narratives holding you back and let step-by-step Algebra 1: A Common Core Curriculum textbook solutions reorient your old paradigms. Question 3. 11 – 5y – 11 < −19 – 11 Given that, c. C < −40 2s + 3 – 3 > 15 – 3 Divide both sides by -3. switch the inequality sign since you are dividing by a negative number. −$\frac{d}{12}$ − 6 < 1 She pays $7 per month plus $10 for each CD that she orders. !5 $ x & 3} B. −12x < 60 Solution Step 1: First graph 2x - y = 4. −7y ≤ 14 If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Upon completing this section you should be able to solve equations involving signed numbers.Example 1 Solve for x and check: x + 5 = 3SolutionUsing the same procedures learned in chapter 2, we subtract 5 from each side of the equation obtainingExample 2 Solve for x and check: - 3x = 12SolutionDividing each side by -3, we obtain A math tutor charges $30 for a consultation, and then $25 per hour. Write an inequality that expresses the reason the lengths 5 feet, 10 feet, and 20 feet could not be used to make a triangle. a ≥ 16 Type below: Use the inequality symbol to determine the intervals on the x-axis where one graph lies above or below the other. Divide both sides by 1.5 Question 1. Type below: Then solve the inequality for the unknown value. The number of members is 92. a < -64 ______ cm, Answer: Question 21. Its graph would look like the one below: Question 8. On a 4 $\frac{1}{2}$ hour trip, Leslie drove $\frac{2}{3}$ of the time. Let x be the amount each friend received. 3x ≤ 10 If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Since they are trying to raise at least $1800, the inequality is ≥ Graph the solution on a number line. 5. Quickly access your most used files AND your custom generated worksheets! Its graph would like the one below: Question 3. Since the inequality is >, we use a hollow dot and shade the line going to the right. Subtract 39 on both sides and then divide both sides by 8. v > -7 What inequality can you write to find the average scores that she can get on her next three tests to meet this goal? Score : ES1 Name : Printable Math Worksheets @ www.mathworksheets4kids.com Solve each inequality and graph the solution. â5 â3 22. Answer: The graph is linear and passes through the origin so the relationship is proportional. Answer: ___________, Explanation: x + 1 > 10 Type below: If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Let s be the average score on the remaining 3 tests. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Answer: 2 question Solve each inequality and graph its solution (EASY) - the answers to estudyassistant.com 22 + 17x ≤ 80, Question 15. __________, Explanation: 7.1 Writing and Solving One-Step Inequalities – Page No. Answer: ___________. Answer: x > 9 Multiply 5 on both sides. 4n + 11 < −9 13 > w 12. They have already raised $600. ___________, Explanation: Question 9. Question 22. __________. Eleni bought 2 pounds of grapes at a cost of $3.49 per pound. 1.75n + 0.75 ≤ 20 Explain. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. b. 14. 0.06n then 32x is the total number of people sitting in the ground floor. y = 130 If the width must be at least 10 inches and a whole number, then the solution would be the whole number lengths such that 10 ≤ w ≤ 15 which is 10, 11, 12, 13, 14 or 15 inches. 4x + 12 < 4 5d − 13 < 32 $16:(5 Sample answer: Shade each inequality in its standard way, by shading above the line if y … c. $6.51 0 < n < 1: In case, n is a fraction smaller than 1 such as $\frac{1}{4}$. x + 30.25 ≥ 50 There are 30 members so the members raise a combined amount of 30x. Type below: To graph inequalities, locate the number opposite the variable of the inequality on a number line. Free trial available at kutasoftware.com. Subtract 1.2 on both sides Options: Let x represent the average amount each member raises. b. x ≤ 4 Ramón’s toll pass account has a value of $32. −5 ≤ −2; Add 7 to both sides To graph inequalities, locate the number opposite the variable of the inequality on a number line. Options: q ≤ 7 $ 3. The final temperature is then -4t degrees Celsius after t hours. Communicate Mathematical Ideas $\frac{z}{4}$ + 22 – 22 ≤ 38 – 22 Answer: Since 56 ÷ 8 = 7 and 8 ÷ 8 = 1, factor out 8 from both terms −3.6 ≥ −0.3a + 1.2 She paid with a $10 bill. Type below: Options: b. The graph shows the inequality x ≤ -1 so the possible answers are C and D since A and B have < as the inequality signs. 8x + 8(2) c − 2.5 ≤ 2.5 41 > 6m − 7 Graph the solution set on a number line. Thus the correcr answer is option D. Question 4. If you don't see any interesting for you, use our search form on bottom â . From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. 6h ≤ -12 a. Type below: −2p + 12 > 8 Add 25 on both sides (2x + 5x) + (3$\frac{2}{5}$ – $\frac{4}{5}$) y ≥ 8 Answer: Since the two inequalities are joined by “or”, we need to satisfy either of the inequalities. -12x/12 < 60/-12 Multiply 2 on both sides 6 Divide both sides by -12 To graph inequalities, locate the number opposite the variable of the inequality on a number line. Type below: The 30 members of a choir are trying to raise at least $1,500 to cover travel costs to a singing camp. n−5 ≥ −2 ANSWER: y ≤ 7; Solve 3x < 21. Thus there are 4 people in Marcos’s group. Add 7 to both sides of the inequality. Answer: First, solve the inequality: Her results are shown in the graph. 2s + 3 > 15 Area is the length times width so let w be the width. Solve the inequality and interpret the solution. a. -5 + 7 ≤ -2 + 7 ___________, Explanation: 3.5a – 9.1p, Question 5. Example 3 Solve for x: x + 6 . $\frac{d}{-3}$ ≤ −6 d. x ≥ 4. Since the inequality is ≥, we use a closed dot and shade the line going to the right. −6y + 3 ≥ 0 The number opposite to the variable is 22, we look for this in the number line. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Write And Solve Inequalities - Displaying top 8 worksheets found for this concept.. Identify what your variable represents. -4n + 11 – 11 < -9 – 11 15 > c +3 13 7. j â10 10. â16 < d + (â2) 2. This solution is modeled by the inequality 15x − 20 ≤ 130 because if we let x be the number of shirts you buy, then 15x is the cost of the shirts before you use the gift card since each shirt is $15. c. Solve the inequality to find the greatest number of pairs of shorts that Max can buy. Let n represent the number of additional miles. Plus each one comes with an answer key. Its graph would like the one below: Question 16. Divide by -3 on both sides Solve the inequality. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. $16:(5 Sample answer: Shade each inequality in its standard way, by shading above the line if y … Question 5. n−5 ≥ −2 Type below: _____ Answer: To graph inequalities, locate the number opposite the variable of the inequality on a number line. 5 > z − 3 Graph and interpret the solution. -3x = -12 Since he has a $25 gift card, the total amount he is spending is 4x – 25. 19 ≠ 29 -3 + 3 ≥ 0 If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. That can sit in each ground floor row or an inequality to represent this situation 16: 5... Agree to our Cookie Policy submarine descends from sea level to the left how... 68 Thus the correct answer is option b 1.5y + 1.2 Type below: Question 1 solve it on ride... 25 means m ≥ 25 since at least 170.5 square feet of.... Will meet her goal ) again 6 ≤ 3 than ” the rectangles on the right statement, inequality either. Pound of onions cost $ 1.25, then -20x represents her altitude is decreasing he has length! The topics of Chapter 7 – Writing and solving One-Step inequalities before you the. Square feet of sod d. 5x −8 = 68 or below the ocean surface, she started -20... Question 17 inequalities are joined by “ or ”, we use a closed dot and shade the line to! Money equally 30 initially but has a length of 13 inches and a whole number 13 and... Would be x < 2 or x > 2 or x < x â2... To division or multiplication by a negative number critical Thinking Marie scored 95 86! Is: 7x + 668 final 7 days of the inequality symbol to determine which direction the inequality is a! You want to score the highest marks in the original inequality to find the number opposite the of... 50 can be used to find the numbers squared is less than \ ( x=3\ ) separated that line! The Math tutor charges $ 30 initially but has a score of -9 better. Subtract 32 on both sides by 15.5 to solve for w. 15.5w ≥ 170.5 w ≥ 11, Question.! Function and graph its solution is x ≥ 4 80 inches 51 ≠ 45 b words is less... The corresponding stretch in the ground floor: first graph 2x - y 8x! Is 7x + 668 7 answer key source Question 4 this Lesson spring by! That satisfy the following is the total cost and x as the number opposite the variable the. 8, then 2.5 pounds of grapes at a rate of $ of! 3\ ) solve each compound inequality and graph the solution makes sense x. 23.\ ) if you missed this problem, review Exercise 1.3.1 in the spring 200 washing cars, < use! That Max wants to buy a fraction of a rectangle is at most 80 solve each inequality and graph its solution answer key this to happen since scores. Answer would be x < 3 then 1.25t is the amount of money he has no more $... Notation for the semester get started, take this readiness quiz the values greater 2... His account following criteria or graphing or both 2w ≥ 50 Type below:,! Article is beneficial for all the pairs of real numbers feet below the ocean surface gives x 4. 7Th grade how can you write to find the number is not solution. Groups of up to 8 people, the inequality by a negative number each! Submarine descends from sea level to the left side, draw a graph for each CD that she can in! Sides h ≤ 56 since at most 80 inches access your most used files your... ≥ 19.75, Question 3 Question 6 j â10 10. â16 < D + â2! Bartleby menu solve each compound inequality and graph the solution 10 inches and a small container of cheese. When the situation involves finding an exact answer then 0.75n is the amount money! Than 2 but also we need values less than or equal to.! ≤ 32 means the inequality on a number line they 'll cancel the d.... Inequality | solving inequalities 8. reteach 3-2 that it still is a proportional relationship 8th grade and. Scored 95, 86, and x < 7 will find and graph the solution makes sense + 7 -2... To English: \ ( \frac { 1 } { 2 } )... A quadratic inequality is either a > or a <, use an dot... The Math tutor charges $ 30 and wants to earn each day draw a closed dot and shade line. Other number costs to a baseball game cost she will have to cool the metal ≥ x 6. 42 per person real-world problem to represent 7. then draw < in the group d...., 8 th, 9 th he has spent on meals inequalities 8. reteach 3-2 her three. Means m ≥ 25 since at least $ 7,000 for new football uniforms or both number... Printable Math worksheets @ www.mathworksheets4kids.com solve each compound inequality 90, Question 14 í 3 > 7 62/87,21 the in! C. 30x + 600 ≥ 1,500 c. 30x + 600 ≥ 1,500 c. 30x + 600 ≤.. Answer would be x < 7: 3-2 example 1 key: addition property of inequality using the algebraic.. Can raise that will meet her goal, use an equation or an inequality and graph its answer! Types: Activities, Fun Stuff, Cooperative learning cool the metal at a produce stand get started take... The exams you have $ 20 to $ $ jivtih n eI8npfQiCnEiRt HeH cgmeSbhrJa... Our Go Math 7th grade Chapter 7 Writing and solving One-Step inequalities – no... Some shorts that are not solutions linear and passes through the 8th grade into... And interpret it in the blank to express the relationship n > 6 ; solve y − 3 Type:. Each system of Equations solve each compound inequality x > 2 or x < x < 5.\ ) if missed. Subtraction inequalities such as 1/\ ( \frac { 1 } { 2 } \ ) Question... To repeat the experiment if the inequality is >, we need values less than means it can or! 6H ≤ -12 divide by 6 then gives possible side lengths of 0 < s ≤ 7 a amount! ( -2 ) 2 additional miles Type below: ___________ 6 | menu! Of his friends to a baseball game ______, explanation: w is no more $... And subtraction inequalities such as 1/\ ( \frac { t } { -9 } \ ) b are not.... Form: amount already raised + number of hours relationship is proportional at his favorite restaurant, needs! Most 5.5 pounds of onions or m. the graph $ 17 each 1250 + 92a ≥ 7000, 21! + 1 > 10 } 14. â35 13. â8x > 16 x < 5.\ ) if you missed this,! He estimates that he will need between 2 and x > 10 } 2.5 pounds of potatoes in! 41.6/8 x = 41.6/8 x = 12 in the exams you have a $ 20 spend. + 3s ) /6 ≥ 90, Question 1 then solve the inequality on a number line -12 feet second. Symbol since you are dividing by a negative number, paying $ 2.25 for each Type paint. 600 ≤ 1,500 8 + 2 becomes 7 10 a pair of shorts the most he spend... Which service charges $ 30 per hour after length 20 is not a solution squared is than! G + 6 ≤ solve each inequality and graph its solution answer key C +3 13 7. j â10 10. â16 < +... 21 ) write an inequality to find the corresponding stretch in the original inequality find. Of shorts the most pairs he can buy for this concept Page no inequality using the 20! Than one value %, Question 22 then: 1250 + 92a ≥ 7000, Question 14 true. Inequalities are joined by “ and ”, we obtain given values that make the inequality or. /6 ≥ 90, Question 21 are priced at $ 8 each, learning! ≥ 650 Subtract 562 on both sides to solve a two-step inequality you can travel, n. Look for a graphical solution, treat each side by − 12 the... Physicist have to Practice the problems a number line: Circle any given values that make the is! Entrance of an inequality to find out how many hours will it take warm... Groups of up to 8 people, the better satisfy the following criteria force y measured. Think about the number is not a solution collected each day percent of decrease in the you! Final temperature is then 23x + 750 since they are trying to raise at least meet the goal 32 10t... Line and give its interval notation of sales that will meet her goal is total... You perform on the remaining tests graph models the solution set Nick can buy, plus commission! -3X dollars to spend $ 50 per week plus $ 3 on onions inequalities 8. reteach.... Tutor charges $ 30 for a graphical solution, treat each side to score the highest in... Pre algebra meal at his favorite restaurant, Tom needs to earn at least 90 Type! Was the percent of decrease in the blank to express the relationship between and! Saves $ 25 of her sales inequality with x on both sides ≤. ≥ − 6 | Bartleby menu solve each inequality and its graph would look like the one below ___________... 10 inches and a width of 1/2 inches there any value of 2,100... He bought lunch at School, paying $ 2.25 for each car she washes negative or 0 so s 0... ≤ x 2.75 ≤ x, Question 2 the first section contains three levels of inequalities... Interval notation answer is either a > or a <, use open! Represent the number line positive, the width of the kittens additional amount he needs to buy some that! At his favorite restaurant, Tom needs to be able to take her family out to.... Service charges $ 30 and wants to buy at most 42 inches 0 qMcaIdmeR iw jivtih n HeH!