Question

Solve the equation $$ 5 x-(6-x)=2(x-7) $$

Short answer

The solution to the equation is \( x = -2 \)

Step-by-step solution

Simplify the equation

Start by simplifying the left-hand side of the equation. The expression 5x - (6 - x) can be simplified by distributing the negative sign over the terms within the brackets to get 5x - 6 + x. After simplifying, the left side of the equation becomes 6x - 6.

Simplify the right-hand side of the equation

The right-hand side of the equation is 2(x - 7). Distribute 2 over (x - 7) to get 2x - 14.

Write the simplified equation

After simplifying both sides, the equation now reads 6x - 6 = 2x - 14.

Solve for x

To solve for x, start by moving like terms together. Subtract 2x from both sides to get 4x - 6 = -14. Then add 6 to both sides to get 4x = -8. Divide both sides by 4 to isolate x, which gives x = -2.