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Simplifying 3[z + -1(9z + 13) + 5] = 2(z + 1) Reorder the terms: 3[z + -1(13 + 9z) + 5] = 2(z + 1) 3[z + (13 * -1 + 9z * -1) + 5] = 2(z + 1) 3[z + (-13 + -9z) + 5] = 2(z + 1) Reorder the terms: 3[-13 + 5 + z + -9z] = 2(z + 1) Combine like terms: -13 + 5 = -8 3[-8 + z + -9z] = 2(z + 1) Combine like terms: z + -9z = -8z 3[-8 + -8z] = 2(z + 1) [-8 * 3 + -8z * 3] = 2(z + 1) [-24 + -24z] = 2(z + 1) Reorder the terms: -24 + -24z = 2(1 + z) -24 + -24z = (1 * 2 + z * 2) -24 + -24z = (2 + 2z) Solving -24 + -24z = 2 + 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. -24 + -24z + -2z = 2 + 2z + -2z Combine like terms: -24z + -2z = -26z -24 + -26z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -24 + -26z = 2 + 0 -24 + -26z = 2 Add '24' to each side of the equation. -24 + 24 + -26z = 2 + 24 Combine like terms: -24 + 24 = 0 0 + -26z = 2 + 24 -26z = 2 + 24 Combine like terms: 2 + 24 = 26 -26z = 26 Divide each side by '-26'. z = -1 Simplifying z = -1
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