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Simplifying 3[z + -1(10z + 71) + 8] = 3(z + 7) Reorder the terms: 3[z + -1(71 + 10z) + 8] = 3(z + 7) 3[z + (71 * -1 + 10z * -1) + 8] = 3(z + 7) 3[z + (-71 + -10z) + 8] = 3(z + 7) Reorder the terms: 3[-71 + 8 + z + -10z] = 3(z + 7) Combine like terms: -71 + 8 = -63 3[-63 + z + -10z] = 3(z + 7) Combine like terms: z + -10z = -9z 3[-63 + -9z] = 3(z + 7) [-63 * 3 + -9z * 3] = 3(z + 7) [-189 + -27z] = 3(z + 7) Reorder the terms: -189 + -27z = 3(7 + z) -189 + -27z = (7 * 3 + z * 3) -189 + -27z = (21 + 3z) Solving -189 + -27z = 21 + 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. -189 + -27z + -3z = 21 + 3z + -3z Combine like terms: -27z + -3z = -30z -189 + -30z = 21 + 3z + -3z Combine like terms: 3z + -3z = 0 -189 + -30z = 21 + 0 -189 + -30z = 21 Add '189' to each side of the equation. -189 + 189 + -30z = 21 + 189 Combine like terms: -189 + 189 = 0 0 + -30z = 21 + 189 -30z = 21 + 189 Combine like terms: 21 + 189 = 210 -30z = 210 Divide each side by '-30'. z = -7 Simplifying z = -7
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