Question

1. \\(\frac{2}{3}(x + 7) = 6\\)

Explanation:

Step1: Eliminate the fraction

Multiply both sides of the equation $\frac{2}{3}(x + 7)=6$ by $\frac{3}{2}$ to get rid of the fraction on the left side.
$$\frac{3}{2}\times\frac{2}{3}(x + 7)=\frac{3}{2}\times6$$
Simplifying the left side, the $\frac{3}{2}$ and $\frac{2}{3}$ cancel out, leaving $x + 7$. On the right side, $\frac{3}{2}\times6 = 9$. So the equation becomes $x + 7=9$.

Step2: Solve for x

Subtract 7 from both sides of the equation $x + 7=9$.
$$x+7 - 7=9 - 7$$
Simplifying both sides, we get $x = 2$.

Answer:

$x = 2$