Question

solve the inequality 12 - 8x < 52

Explanation:

Step1: Subtract 12 from both sides

To isolate the term with \( x \), we subtract 12 from both sides of the inequality \( 12 - 8x < 52 \). This gives us \( 12 - 12 - 8x < 52 - 12 \), which simplifies to \( -8x < 40 \).

Step2: Divide by -8 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. So, we divide both sides of \( -8x < 40 \) by -8. This gives \( \frac{-8x}{-8} > \frac{40}{-8} \) (note the reversed inequality), which simplifies to \( x > -5 \).

Answer:

\( x > -5 \)