Question

An equation is shown below. 12 – 6(w – 3) = 3(– 5 – 3w) + 21 Enter the solution of w for this equation.

Answer 1

Simplifying
12 + -6(w + -3) = 3(-5 + -3w) + 21

Reorder the terms:
12 + -6(-3 + w) = 3(-5 + -3w) + 21
12 + (-3 * -6 + w * -6) = 3(-5 + -3w) + 21
12 + (18 + -6w) = 3(-5 + -3w) + 21

Combine like terms: 12 + 18 = 30
30 + -6w = 3(-5 + -3w) + 21
30 + -6w = (-5 * 3 + -3w * 3) + 21
30 + -6w = (-15 + -9w) + 21

Reorder the terms:
30 + -6w = -15 + 21 + -9w

Combine like terms: -15 + 21 = 6
30 + -6w = 6 + -9w

Solving
30 + -6w = 6 + -9w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '9w' to each side of the equation.
30 + -6w + 9w = 6 + -9w + 9w

Combine like terms: -6w + 9w = 3w
30 + 3w = 6 + -9w + 9w

Combine like terms: -9w + 9w = 0
30 + 3w = 6 + 0
30 + 3w = 6

Add '-30' to each side of the equation.
30 + -30 + 3w = 6 + -30

Combine like terms: 30 + -30 = 0
0 + 3w = 6 + -30
3w = 6 + -30

Combine like terms: 6 + -30 = -24
3w = -24

Divide each side by '3'.
w = -8

Simplifying
w = -8