Question

solve the inequality 31 > 7 - 3x

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we first subtract 7 from both sides of the inequality \( 31 > 7 - 3x \). This gives us \( 31 - 7 > 7 - 3x - 7 \), which simplifies to \( 24 > -3x \).

Step2: Divide by -3 (reverse inequality)

Next, we divide both sides by -3. When dividing an inequality by a negative number, we must reverse the inequality sign. So, dividing \( 24 > -3x \) by -3 gives \( \frac{24}{-3} < \frac{-3x}{-3} \), which simplifies to \( -8 < x \) or \( x > -8 \).

Answer:

\( x > -8 \)