1.65 + 0.85x = 20 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 >. 7 – 7 > -4 – 7 He decided to buy a pair of sneakers for $39, but the total cost of the shorts and the sneakers must be less than $75. Solve the inequality first: Question 9. The number opposite the variable is -5, we look for this in the number line. Recognize the Relation Between the Solutions of an Inequality and its Graph. Students will cut apart 20 cards, solve each inequality, and make matching sets of cards that have the same solution. Since the inequality is >, we use a hollow dot and shade the line going to the right. Which graph models the solution of the inequality −6 ≤ −3x? If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Show your work. 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 >. A real-world problem could be: The temperature of a metal is currently at -18°C. Its graph would like the one below: Question 13. Answer: ANSWER: n > 6; Solve y − 3 ≤ 4. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. ANSWER: y ≤ 7; Solve 3x < 21. Add 25 on both sides To plot -6 on the number line, from 0, we move 6 units to the left. To graph inequalities, locate the number opposite the variable of the inequality on a number line. ___________. 6h ≤ -12 ___________, Explanation: Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. Answer: B.!2 $ y & 3. __________. Joseph used the problem-solving strategy Work Backward to solve the inequality 2n + 5 < 13. Identify what your variable represents. a. If you don’t switch the inequality sign you would get x ≤ 0 which means the inequality would be true for all non-positive numbers 193 + y ≥ 201 Graph the solution on a number line. He has already spent $30.25. 5 + 2 8 + 2 becomes 7 10. Let x represent the number of shirts he can buy then 17x is the total cost of the shirts and 22 + 17x is the total cost Write and solve an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. $16:(5 Sample answer: Shade each inequality in its standard way, by shading above the line if y … C < −\(\frac{40}{9}\) The number opposite to the variable is 22, we look for this in the number line. b. Question 26. Also, if you are on a PC, hold down your alt key, type 242 on the number pad (with num lock on), then let go of the alt. 0.7(5a − 13p) The vet says that Lena’s puppy will grow to be at most 28 inches tall. ___________. Substitute x = 12 in the above equation. ______ pairs of shoes, Explanation: To plot 9 on a number line, from 0, we move 9 units to the right. Since you can’t buy a fraction of a pair of shorts the most pairs he can buy is 4. To plot a point, starting from 0, count the number of units going to the left or right. He has no more than $24 to spend on snacks. The sign shows some prices at a produce stand. 10 + \(\frac{g}{-9}\) > 12 d. 0.85x − 1.65 = 20. n < 5 Each time he uses the toll road, $1.25 is deducted from the account. −1.25t + 32 < 10 __________, Explanation: Answer: 2 question Solve each inequality and graph its solution (EASY) - the answers to estudyassistant.com 2s + 5 ≥ 49 h ≤ -2, Question 1. Graph the solution set of the inequality and interpret it in the context of the problem. 23x + 750 > 1,800 2s + 5 – 5 ≥ 49 – 5 Solve each compound inequality and graph its solution. Question 1. (−0.5x − 4) − (1.5x + 2.3) −6y + 3 ≥ 0 k is no greater than 9 means k ≤ 9 since no greater means it can equal or must be smaller. Its graph would like the one below: Question 9. divide both sides by 3 to solve for x. Let t represent the number of hours. First, solve the inequality: Add 28 on both sides Type below: First, solve the inequality: x y x í 3 62/87,21 *UDSK HDFK LQHTXDOLW\ The graph of x LV VROLG DQG LV LQFOXGHG LQ WKH JUDSK RI WKH VROXWLRQ The graph of y x í 3 is also solid and is included in the graph of the solution. Question 2. She wants a score of -9 or better and since smaller scores are better, the inequality is ≤. 4% -0.5x – 1.5x – 4 – 2.3 ___________. To graph inequalities, locate the number opposite the variable of the inequality on a number line. Divide both sides by -0.3 −2p + 12 > 8 Answer: The final temperature is then -4t degrees Celsius after t hours. c. 23x + 750 < 1,800 Thus the correct answer is option D. Question 11. Chet needs to buy 4 work shirts, all costing the same amount. Divide both sides by 7. ___________. The inequalities include both positive and negative numbers, including ones that r . If we add -6 to each side, we obtain. 2x + 5 – 5 ≤ 1 – 5 Write an inequality to find how many CDs she can purchase in a month if she spends no more than $100. __________. a. 30x + 600 ≥ 1,500 __________. −3.6 ≥ −0.3a + 1.2 Type below: An online tutoring service charges $30 per hour. Since they have already raised $600, the total amount raised 30x + 600 they need to raise at least $1500 so the inequality is ≥. The sides of the hexagon shown are equal in length. Type below: The inequality \(\frac{9}{5}\)C + 32 < −40 can be used to find Celsius temperatures that are less than -40° Fahrenheit. d. C < −\(\frac{72}{5}\). Explain. This leaves 9 positive squares on the right side. Type below: 8x + 16 Type below: 8x − 28 = 44 Describe the steps you would follow to write a two-step inequality you can use to solve a real-world problem. Lionel wants to buy a belt that costs $22. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. ___________, Explanation: How much more does Tom need to spend to get his free meal? John says that if one side of an inequality is 0, you don’t have to reverse the inequality symbol when you multiply or divide both sides by a negative number. Question 7. \(\frac{d}{-3}\) ≤ −6 Multiply the two fractions by first writing 4 \(\frac{1}{2}\) as an improper fraction then cancel the 2s and then simplifying the division. ___________. Write an inequality that expresses the reason the lengths 5 feet, 10 feet, and 20 feet could not be used to make a triangle. Suppose you are solving an inequality. 12a > —6z < -18 —2 —20 x > 12 16. —12 < 4a 2k —4, Solving Equations, Inequalities & Absolute Values Solve each equation. The interpretation of this solution is that width must be a positive real number that is at most 15 inches. 21) Write an inequality with x on both sides whose solution is x ≥ 2 Many answers. Explanation: Question 9. Divide -4 by both sides Solve, graph, and give interval notation for the inequality . -6(1) + 3 ≥ 0 Answer: Options: After solving an inequality, it is often helpful to check some points to see if the solution makes sense. Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. ___________, Explanation: Combine the lilke terms Answer: $ 3. For a graphical solution, treat each side of the inequality as a function and graph the two functions. Divide both sides by -9 Answer: Both involve using the same operations. 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