Solving Linear Equations

Problem 252: Solve the equation $2(6-x) = 3(-4 + 2x) + 5$ .

Solution: Let’s “get rid of” the parentheses first.

$2(6-x) = 3(-4 + 2x) + 5 \implies 12 - 2x = -12 + 6x + 5$

Next, we will combine like terms.

$12 - 2x = -12 + 6x + 5 \implies 12 - 2x = 6x - 7$

Simplify by combining line terms.

$12 - 2x = 6x - 7 \implies -2x - 6x = - 7 -12 \implies -8x = -19$

Solve for $x$ .

$-8x = -19 \implies x = \frac{19}{8}$