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Simplifying 7[z + -1(5z + 18) + 2] = 3(z + 4) Reorder the terms: 7[z + -1(18 + 5z) + 2] = 3(z + 4) 7[z + (18 * -1 + 5z * -1) + 2] = 3(z + 4) 7[z + (-18 + -5z) + 2] = 3(z + 4) Reorder the terms: 7[-18 + 2 + z + -5z] = 3(z + 4) Combine like terms: -18 + 2 = -16 7[-16 + z + -5z] = 3(z + 4) Combine like terms: z + -5z = -4z 7[-16 + -4z] = 3(z + 4) [-16 * 7 + -4z * 7] = 3(z + 4) [-112 + -28z] = 3(z + 4) Reorder the terms: -112 + -28z = 3(4 + z) -112 + -28z = (4 * 3 + z * 3) -112 + -28z = (12 + 3z) Solving -112 + -28z = 12 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -112 + -28z + -3z = 12 + 3z + -3z Combine like terms: -28z + -3z = -31z -112 + -31z = 12 + 3z + -3z Combine like terms: 3z + -3z = 0 -112 + -31z = 12 + 0 -112 + -31z = 12 Add '112' to each side of the equation. -112 + 112 + -31z = 12 + 112 Combine like terms: -112 + 112 = 0 0 + -31z = 12 + 112 -31z = 12 + 112 Combine like terms: 12 + 112 = 124 -31z = 124 Divide each side by '-31'. z = -4 Simplifying z = -4
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