Question

what is the solution to the inequality $\frac{1}{2}(5x - 8)>3(x + 3)$?
a. $x < - 26$
b. $x > - 26$
c. $x < - 14$
d. $x > - 14$

Explanation:

Step1: Expand both sides

$\frac{1}{2}(5x - 8)=\frac{5}{2}x-4$ and $3(x + 3)=3x+9$. So the inequality becomes $\frac{5}{2}x-4>3x + 9$.

Step2: Move terms with x to one - side

Subtract $3x$ from both sides: $\frac{5}{2}x-3x-4>3x-3x + 9$, which simplifies to $\frac{5}{2}x-\frac{6}{2}x-4>9$, or $-\frac{1}{2}x-4>9$.

Step3: Move the constant term

Add 4 to both sides: $-\frac{1}{2}x-4 + 4>9 + 4$, getting $-\frac{1}{2}x>13$.

Step4: Solve for x

Multiply both sides by - 2 and reverse the inequality sign. So $x<-26$.

Answer:

A. $x < - 26$