Question

Solve the equation $$ 8=-\frac{2}{3}(2 x-6) $$

Short answer

The solution of the equation \( 8=-\frac{2}{3}(2 x-6) \) is \( x = -3 \)

Step-by-step solution

Distributive Property

Apply the distributive property of multiplication over subtraction to solve inside the parentheses. Therefore, the equation becomes \( 8=-\frac{2}{3}*2x + \frac{2}{3}*6 \). This simplifies to \( 8=-\frac{4}{3}x + 4 \).

Isolate the x variable

Start to isolate x by subtracting 4 from both sides of the equation. Therefore, the equation becomes \( 8-4=-\frac{4}{3}x + 4-4 \) which simplifies to \( 4 = -\frac{4}{3}x \).

Solve for x

Now, solve for x by dividing each side by -4/3 (or multiplying by -3/4). The equation becomes \( 4*-\frac{3}{4} = x \) simplifying further to \( x=-3 \).

Checking the solution

Substitute x = -3 into the original equation to verify that it is correct solution. Left-hand side \( = 8 \) and right-hand side \( = -\frac{2}{3}(2*(-3)-6) = -\frac{2}{3}*(-6) = 8 \). Since left-hand side equals right-hand side, x = -3 is the solution.