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Simplifying 4(3w + -1) + 2 = 18 + -2(3w + 1) Reorder the terms: 4(-1 + 3w) + 2 = 18 + -2(3w + 1) (-1 * 4 + 3w * 4) + 2 = 18 + -2(3w + 1) (-4 + 12w) + 2 = 18 + -2(3w + 1) Reorder the terms: -4 + 2 + 12w = 18 + -2(3w + 1) Combine like terms: -4 + 2 = -2 -2 + 12w = 18 + -2(3w + 1) Reorder the terms: -2 + 12w = 18 + -2(1 + 3w) -2 + 12w = 18 + (1 * -2 + 3w * -2) -2 + 12w = 18 + (-2 + -6w) Combine like terms: 18 + -2 = 16 -2 + 12w = 16 + -6w Solving -2 + 12w = 16 + -6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6w' to each side of the equation. -2 + 12w + 6w = 16 + -6w + 6w Combine like terms: 12w + 6w = 18w -2 + 18w = 16 + -6w + 6w Combine like terms: -6w + 6w = 0 -2 + 18w = 16 + 0 -2 + 18w = 16 Add '2' to each side of the equation. -2 + 2 + 18w = 16 + 2 Combine like terms: -2 + 2 = 0 0 + 18w = 16 + 2 18w = 16 + 2 Combine like terms: 16 + 2 = 18 18w = 18 Divide each side by '18'. w = 1 Simplifying w = 1
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