Question

where/what is the mistake?
line 4 - you should multiply both sides by 3/2.
line 5 - there was a calculation error.
line 2 - you should add 12 both sides.
$\frac{2}{3}x + 12 = 18$
$\frac{2}{3}x+12 - 12 = 18 - 12$
$\frac{2}{3}x = 6$
$\frac{3}{2}cdot\frac{2}{3}x = 6cdot\frac{2}{3}$
$x = 4$

Explanation:

Step1: Analyze the steps to solve the equation

We start with the equation $\frac{2}{3}x + 12=18$. Subtracting 12 from both sides in line 2 is correct: $\frac{2}{3}x+12 - 12=18 - 12$ gives $\frac{2}{3}x = 6$.

Step2: Identify the error in line 4

To isolate $x$ in $\frac{2}{3}x = 6$, we should multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$. But in the given solution, the right - hand side is multiplied by $\frac{2}{3}$ instead of $\frac{3}{2}$.

Answer:

Line 4 - You should multiply both sides by 3/2.