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Simplifying 7[z + -1(3z + 29) + 9] = 2(z + 10) Reorder the terms: 7[z + -1(29 + 3z) + 9] = 2(z + 10) 7[z + (29 * -1 + 3z * -1) + 9] = 2(z + 10) 7[z + (-29 + -3z) + 9] = 2(z + 10) Reorder the terms: 7[-29 + 9 + z + -3z] = 2(z + 10) Combine like terms: -29 + 9 = -20 7[-20 + z + -3z] = 2(z + 10) Combine like terms: z + -3z = -2z 7[-20 + -2z] = 2(z + 10) [-20 * 7 + -2z * 7] = 2(z + 10) [-140 + -14z] = 2(z + 10) Reorder the terms: -140 + -14z = 2(10 + z) -140 + -14z = (10 * 2 + z * 2) -140 + -14z = (20 + 2z) Solving -140 + -14z = 20 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -140 + -14z + -2z = 20 + 2z + -2z Combine like terms: -14z + -2z = -16z -140 + -16z = 20 + 2z + -2z Combine like terms: 2z + -2z = 0 -140 + -16z = 20 + 0 -140 + -16z = 20 Add '140' to each side of the equation. -140 + 140 + -16z = 20 + 140 Combine like terms: -140 + 140 = 0 0 + -16z = 20 + 140 -16z = 20 + 140 Combine like terms: 20 + 140 = 160 -16z = 160 Divide each side by '-16'. z = -10 Simplifying z = -10
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