Solve |5x + 3| ≤ 7: Absolute Value Inequality Analysis

Given:

$\left|5x + 3\right| \leq 7$

Which of the following statements is necessarily true?

To solve $\left| 5x + 3 \right| \leq 7$, consider both cases:$5x + 3 \leq 7$ and $5x + 3 \geq -7$.

1. Solving $5x + 3 \leq 7$:

$5x + 3 \leq 7$

Subtract 3 from both sides:

$5x \leq 4$

Divide both sides by 5:

$x \leq 0.8$

2. Solving $5x + 3 \geq -7$:

$5x + 3 \geq -7$

Subtract 3 from both sides:

$5x \geq -10$

Divide both sides by 5:

$x \geq -2$

Combining both results, we find $-2 \leq x \leq 0.8$.