1. 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.

2. Solve One-Step Inequalities
Lesson 8-7

3. 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.

4. Example 1
Solve x + 7 ≥ 10. Graph the solution on a number line. Use inverse operations. x + 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.”

5. Example 2
Solve x – 3 < 9. Graph the solution on the number line. Use inverse operations. x – 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.

6. Got It? Solve and graph the inequality. 1) n + 2 ≤ 5 2) y – 3 >9

7. 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.”.

8. Example 4
Solve 𝑥 8 > 3. Graph the solution on a number line. 𝑥 8 > 3 𝑥 8 (8) > 3 (8) x > 24

9. Got It? Solve and graph the inequality. 3) 10x < 80 4) 𝑥 6 ≥ 7
4) 𝑥 6 ≥ 7

10. 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.

11. Homework Hint
#6a x (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?