Question

find the solution set of the inequality
52 - 3x < -14.
x

Explanation:

Step1: Subtract 52 from both sides

To isolate the term with \( x \), we subtract 52 from both sides of the inequality \( 52 - 3x < -14 \). This gives:
\( 52 - 3x - 52 < -14 - 52 \)
Simplifying both sides, we get:
\( -3x < -66 \)

Step2: Divide by -3 (reverse inequality)

When dividing an inequality by a negative number, the direction of the inequality sign reverses. So we divide both sides of \( -3x < -66 \) by -3:
\( \frac{-3x}{-3} > \frac{-66}{-3} \)
Simplifying both sides, we find:
\( x > 22 \)

Answer:

\( x > 22 \)