Question

if $3(x - 4) = -2(2x + 7)$, then what is the value of $3x$?
hint: begin by applying the distributive property to both sides of the equal sign
\bigcirc -1
\bigcirc -\frac{2}{7}
\bigcirc -\frac{6}{7}
\bigcirc \frac{2}{7}

Explanation:

Step1: Apply Distributive Property

$3(x-4) = -2(2x+7)$ expands to $3x - 12 = -4x - 14$

Step2: Isolate x terms on left

Add $4x$ to both sides: $3x + 4x - 12 = -14$ → $7x - 12 = -14$

Step3: Isolate constant terms on right

Add 12 to both sides: $7x = -14 + 12$ → $7x = -2$

Step4: Solve for x

Divide by 7: $x = \frac{-2}{7}$

Step5: Calculate 3x

Multiply x by 3: $3x = 3 \times \frac{-2}{7} = \frac{-6}{7}$

Answer:

$\boldsymbol{-\frac{6}{7}}$ (matches the third option)