Question

1. $-\frac{3(x + 2)}{3}+\frac{2}{3}x=-\frac{5}{4}x + 2$

Explanation:

Step1: Expand the left - hand side

$-\frac{3(x + 2)}{3}+\frac{2}{3}x=-\frac{3x+6}{3}+\frac{2}{3}x=-x - 2+\frac{2}{3}x$.

Step2: Combine like - terms on the left - hand side

$-x+\frac{2}{3}x-2=(-1+\frac{2}{3})x-2=-\frac{1}{3}x - 2$.

Step3: Move all terms with $x$ to one side

$-\frac{1}{3}x+\frac{3}{4}x=2 + 2$.

Step4: Find a common denominator for $x$ terms

The common denominator of 3 and 4 is 12. So $-\frac{1}{3}x+\frac{3}{4}x=\frac{-4x + 9x}{12}=\frac{5}{12}x$. And $2 + 2 = 4$.

Step5: Solve for $x$

$x=4\times\frac{12}{5}=\frac{48}{5}$.

Answer:

$x = \frac{48}{5}$