Solve the inequality $|5-4x| \le 15$.

1. Problem Description

Solve the inequality $|5-4x| \le 15$.

2. Solution Steps

To solve the inequality $|5 - 4x| \le 15$, we need to consider two cases:

Case 1: $5 - 4x \le 15$

$5 - 4x \le 15$

Subtract 5 from both sides:

$-4x \le 15 - 5$

$-4x \le 10$

Divide both sides by -4 (and reverse the inequality sign since we are dividing by a negative number):

$x \ge \frac{10}{-4}$

$x \ge -\frac{5}{2}$

Case 2: $-(5 - 4x) \le 15$

$-5 + 4x \le 15$

Add 5 to both sides:

$4x \le 15 + 5$

$4x \le 20$

Divide both sides by 4:

$x \le \frac{20}{4}$

$x \le 5$

Combining the two inequalities, we have $-\frac{5}{2} \le x \le 5$. This can also be written as $-2.5 \le x \le 5$.

3. Final Answer

$-\frac{5}{2} \le x \le 5$

or

$-2.5 \le x \le 5$