Question

Solve the inequality -5/2 (3x-2) < 6-2x. You will need to show and explain every step. You may add more lines if you need them.(I’ve took a picture of the question as well)

Answer 1

Given:

$-\frac{5}{2}(3x-2)<6-2x$

Step 1: Simplify the equation by multiplying -5/2 to the variables inside the parenthesis.

$\begin{gathered} -\frac{5}{2}(3x-2)<6-2x \\ -\frac{15x}{2}+5<6-2x \end{gathered}$

Step 2: Subtract 5 from both sides.

$\begin{gathered} -\frac{15x}{2}+5<6-2x \\ -\frac{15x}{2}+5-5<6-2x-5 \\ -\frac{15x}{2}<1-2x \end{gathered}$

Step 3: Add 2x to both sides.

$\begin{gathered} -\frac{15x}{2}<1-2x \\ -\frac{15x}{2}+2x<1-2x+2x \\ -\frac{11x}{2}<1 \end{gathered}$

Step 4: Multiply both sides by -1 and reverse the inequality.

$\begin{gathered} -\frac{11x}{2}<1 \\ -\frac{11x}{2}\cdot(-1)<1\cdot(-1) \\ \frac{11x}{2}>-1 \end{gathered}$

Step 5: Divide both sides by 11/2.

$\begin{gathered} \frac{11x}{2}>-1 \\ \frac{\frac{11x}{2}}{\frac{11}{2}}>\frac{-1}{\frac{11}{2}} \\ x>-\frac{2}{11} \end{gathered}$

ANSWER:

$x>-\frac{2}{11}$