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Simplifying 7[z + -1(5z + 20) + 8] = 5(z + 3) Reorder the terms: 7[z + -1(20 + 5z) + 8] = 5(z + 3) 7[z + (20 * -1 + 5z * -1) + 8] = 5(z + 3) 7[z + (-20 + -5z) + 8] = 5(z + 3) Reorder the terms: 7[-20 + 8 + z + -5z] = 5(z + 3) Combine like terms: -20 + 8 = -12 7[-12 + z + -5z] = 5(z + 3) Combine like terms: z + -5z = -4z 7[-12 + -4z] = 5(z + 3) [-12 * 7 + -4z * 7] = 5(z + 3) [-84 + -28z] = 5(z + 3) Reorder the terms: -84 + -28z = 5(3 + z) -84 + -28z = (3 * 5 + z * 5) -84 + -28z = (15 + 5z) Solving -84 + -28z = 15 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -84 + -28z + -5z = 15 + 5z + -5z Combine like terms: -28z + -5z = -33z -84 + -33z = 15 + 5z + -5z Combine like terms: 5z + -5z = 0 -84 + -33z = 15 + 0 -84 + -33z = 15 Add '84' to each side of the equation. -84 + 84 + -33z = 15 + 84 Combine like terms: -84 + 84 = 0 0 + -33z = 15 + 84 -33z = 15 + 84 Combine like terms: 15 + 84 = 99 -33z = 99 Divide each side by '-33'. z = -3 Simplifying z = -3
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