Question

solve the following inequality for x.
-7x + 9 > -54
a. x > 9
b. x > 6.43
c. x < 9
d. x < 6.43

Explanation:

Step1: Subtract 9 from both sides

Subtract 9 from each side of the inequality \(-7x + 9 > -54\). This gives \(-7x + 9 - 9 > -54 - 9\), which simplifies to \(-7x > -63\).

Step2: Divide by -7 (reverse inequality)

Divide both sides by -7. When dividing an inequality by a negative number, the inequality sign flips. So \(\frac{-7x}{-7} < \frac{-63}{-7}\), which simplifies to \(x < 9\).

Answer:

C. \( x < 9 \)