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=2 x=−2
2x≥−3

Answer 1

To determine whether the inequality \(2x \geq -3\) is true or false for each given value of \(x\), we will substitute each value into the inequality and see if it holds.

1. **For \(x = 1\)**:
\[
2(1) \geq -3 \implies 2 \geq -3 \quad \text{(True)}
\]

2. **For \(x = 2\)**:
\[
2(2) \geq -3 \implies 4 \geq -3 \quad \text{(True)}
\]

3. **For \(x = -2\)**:
\[
2(-2) \geq -3 \implies -4 \geq -3 \quad \text{(False)}
\]

Now, we can summarize the results in a table format:

| Value of \(x\) | Inequality \(2x \geq -3\) | Result |
|------------------|--------------------------|----------|
| \(1\) | \(2(1) \geq -3\) | True |
| \(2\) | \(2(2) \geq -3\) | True |
| \(-2\) | \(2(-2) \geq -3\) | False |

1. For \(x = 1\), the inequality is **True**.
2. For \(x = 2\), the inequality is **True**.
3. For \(x = -2\), the inequality is **False**.