Warm Up Problem Hannah bought a sweater for $43.99 and there is a 9% sales tax. If Hannah has $50.00 total, does she have enough to buy the sweater? Explain your reasoning.

Solve One-Step Inequalities Lesson 8-7

Objectives I can use inverse operations to solve one-step inequalities. I can explain when to use a closed and open dot when graphing inequalities.

Example 1 Solve x + 7 ≥ 10. Graph the solution on a number line. Use inverse operations. x + 7≥ 10 - 7 - 7 x ≥ 3 The solution is x ≥ 3. To graph it, draw a closed dot at 3 and draw an arrow to the right on the number line. “If you see add, then you subtract.” “If you see subtraction, then you add.” 0 1 2 3 4 5 6 7 8 9

Example 2 Solve x – 3 < 9. Graph the solution on the number line. Use inverse operations. x – 3 < 9 + 3 +3 x < 12 The solution is x < 12. To graph it, draw an open dot on 12 and draw an arrow to the left of the number line. 7 8 9 10 11 12 13 14 15 16

Got It? Solve and graph the inequality. 1) n + 2 ≤ 5 2) y – 3 >9 0 1 2 3 4 5 6 7 8 9 6 7 8 9 10 11 12 13 14 15

Example 3 Solve 5x ≤ 45. Graph the solution on a number line. 5x ≤ 45 5𝑥 5 ≤ 45 5 x ≤ 9 “If you see multiplication, then divide.” “If you see division, then multiply.”. 7 8 9 10 11 12 13 14 15 16

Example 4 Solve 𝑥 8 > 3. Graph the solution on a number line. 𝑥 8 > 3 𝑥 8 (8) > 3 (8) x > 24 21 22 23 24 25 26 27 28 29 30

Got It? Solve and graph the inequality. 3) 10x < 80 4) 𝑥 6 ≥ 7 4) 𝑥 6 ≥ 7 3 4 5 6 7 8 9 10 11 12 38 39 40 41 42 43 44 45 46 47

Example 5 Drew is making bags of party favors for each of the 7 friends attending his birthday party. He does not want to spend more than $42 on the party favors. Write and solve an inequality to find the maximum cost for each party favor bag. Let c represent the cost for each bag of party favors. 7 times the cost of each bag must be no more than $42. 7c ≤ 42 7𝑐 7 ≤ 42 7 c ≤ $6 So Drew can spend a maximum of $6 on each bag.

Homework Hint #6a. 14.50x 32.25 (Fill in the box with an inequality.) The inequality can also be said as “is at most”. #6b. Solve for x. #11. In other words, is there a difference between a < sign and a > sign? If so, what is the difference?