Question

Which values of x make the inequality true or false?
Does each of these values for x make the inequality true or false? Complete the table.
x=1 x=3 x=−2
6x≤−3
Great job!
Now look at this inequality statement. Does each of these values for x make the inequality true or false? Complete the table.
x=1 x=3 x=−2
8≥2+x

Answer 1

Let's evaluate the inequalities one by one for each given value of \( x \).

1. **Inequality: \( 6x \leq -3 \)**

- For \( x = 1 \):
\( 6(1) = 6 \quad \text{(False, since } 6 \leq -3 \text{ is not true)} \)
- For \( x = 3 \):
\( 6(3) = 18 \quad \text{(False, since } 18 \leq -3 \text{ is not true)} \)
- For \( x = -2 \):
\( 6(-2) = -12 \quad \text{(True, since } -12 \leq -3 \text{ is true)} \)

| x | 6x ≤ -3 |
|------|---------|
| 1 | False |
| 3 | False |
| -2 | True |

2. **Inequality: \( 8 \geq 2 + x \)**

- For \( x = 1 \):
\( 2 + 1 = 3 \quad \text{(True, since } 8 \geq 3 \text{ is true)} \)
- For \( x = 3 \):
\( 2 + 3 = 5 \quad \text{(True, since } 8 \geq 5 \text{ is true)} \)
- For \( x = -2 \):
\( 2 + (-2) = 0 \quad \text{(True, since } 8 \geq 0 \text{ is true)} \)

| x | 8 ≥ 2 + x |
|------|-----------|
| 1 | True |
| 3 | True |
| -2 | True |

Here's the completed table for both inequalities:

### 1. For \( 6x \leq -3 \)

| x | 6x ≤ -3 |
|------|---------|
| 1 | False |
| 3 | False |
| -2 | True |

### 2. For \( 8 ≥ 2 + x \)

| x | 8 ≥ 2 + x |
|------|-----------|
| 1 | True |
| 3 | True |
| -2 | True |