1. Warm Up Write as an algebraic expression. Solve. 𝑥+5 =9 3 2𝑥−3 −5=4
1. the product of 12 and the sum of a number and 5
Solve.
2. −2 3𝑦−6 +4 5𝑦−8 =92
𝑥+5 =9
3 2𝑥−3 −5=4

2. 1.5 Solving Inequalities This symbol: < is read as…

3. Solving
Our goal is to have the variable on its own on the left of the inequality sign. Like this…
𝑥<13
𝑦≥−2

4. < How to Solve Solving inequalities is just like solving equations.
One extra detail to pay attention to is the direction of the inequality.
<
BIG
small

5. Safe Things to Do
These are things you can do without affecting the direction of the inequality.
Add or subtract a number from both sides
Multiply or divide both sides by a positive number
Simplify a side

6. Changing Direction
BUT these things will change the direction of the inequality.
Multiply or divide both sides by a negative number
Swapping left and right hand sides.

7. Changing direction means… would become
<
> ≤ ≥
>
< ≥ ≤

8. Solving Inequalities
Get the variable on its own on the left of the inequality sign.
Graph the inequality on a number line.
Open circle: < and >
Closed circle: ≤ and ≥
Arrow pointing right: > and ≥
Arrow pointing left: < and ≤

9. Examples 𝑦−6<3 4𝑥−4>6𝑥+2
Solve each inequality. Then graph the solution set on a number line.
𝑦−6<3
4𝑥−4>6𝑥+2

10. Examples 3𝑎+7≤16 −3𝑛>7𝑛+20 4𝑏−9≤7
Solve each inequality. Then graph the solution set on a number line.
3𝑎+7≤16
−3𝑛>7𝑛+20
4𝑏−9≤7

11. You Try! 5𝑤+3>4𝑤+9 −5𝑦−3<−4𝑦+2
Solve each inequality. Then graph the solution set on a number line.
5𝑤+3>4𝑤+9
−5𝑦−3<−4𝑦+2

12. You Try!
Solve each inequality. Then graph the solution set on a number line.
16−3𝑞<4
3𝑥≥−9

13. Word Problems
An adult panda bear (P) will eat at least 20 pounds of bamboo every day. Write an inequality that expresses this situation.

14. Word Problem
On a Ferris wheel at a carnival, only two people per car are allowed. The two people together cannot weigh more than 300 pounds. Ron and his father want to go on the ride together. Ron’s father weighs 175 pounds.
Write an inequality that expresses this situation.
Draw a visual representation on a number line, and
Solve the inequality to find the maximum weight Ron (𝑥) can be for the two to be allowed on the ride?

15. Word Problem
Rosa’s cell phone plan costs her $50 per month plus $0.25 for each minute she goes beyond her free minutes. How many minutes (𝑚) can she go beyond her free minutes and still pay less than a total of $70?
Write an inequality that expresses this situation.
Draw a visual representation on a number line, and
Solve the inequality.

16. Ticket Out The Door
Write an absolute value equation that corresponds to…
Draw a visual representation on a number line, and
Solve the inequality.
Tara is delivering bags of mulch. Each bag weighs 48 lbs., and the push cart weighs 65 pounds. If her flat-bed truck is capable of hauling 2000 lbs., how many bags of mulch (𝒎) can Tara safely take on each trip?

17. Homework
Lesson 1.5
Pg. 37 #’s 10-21