# Lesson 15

Efficiently Solving Inequalities

### Problem 1

1. Consider the inequality $$\text-1 \leq \frac{x}{2}$$.
1. Predict which values of $$x$$ will make the inequality true.
2. Complete the table to check your prediction.
 $$x$$ $$\frac{x}{2}$$ -4 -3 -2 -1 0 1 2 3 4
2. Consider the inequality $$1 \leq \frac {\text{-}x}{2}$$.
1. Predict which values of $$x$$ will make it true.
2. Complete the table to check your prediction.
 $$x$$ $$\text-\frac{x}{2}$$ -4 -3 -2 -1 0 1 2 3 4

### Solution

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### Problem 2

Diego is solving the inequality $$100-3x \ge \text-50$$. He solves the equation $$100-3x = \text-50$$ and gets $$x=50$$. What is the solution to the inequality?

A:

$$x < 50$$

B:

$$x \le 50$$

C:

$$x > 50$$

D:

$$x \ge 50$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

Solve the inequality $$\text-5(x-1)>\text-40$$, and graph the solution on a number line.

### Solution

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### Problem 4

Select all values of $$x$$ that make the inequality $$\text-x+6\ge10$$ true.

A:

-3.9

B:

4

C:

-4.01

D:

-4

E:

4.01

F:

3.9

G:

0

H:

-7

### Solution

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(From Unit 6, Lesson 13.)

### Problem 5

Draw the solution set for each of the following inequalities.

1. $$x>7$$

2. $$x\geq\text-4.2$$

### Solution

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(From Unit 6, Lesson 13.)

### Problem 6

The price of a pair of earrings is $22 but Priya buys them on sale for$13.20.

1. By how much was the price discounted?
2. What was the percentage of the discount?

### Solution

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(From Unit 4, Lesson 12.)