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Simplifying 2[z + -1(7z + 17) + 5] = 3(z + 2) Reorder the terms: 2[z + -1(17 + 7z) + 5] = 3(z + 2) 2[z + (17 * -1 + 7z * -1) + 5] = 3(z + 2) 2[z + (-17 + -7z) + 5] = 3(z + 2) Reorder the terms: 2[-17 + 5 + z + -7z] = 3(z + 2) Combine like terms: -17 + 5 = -12 2[-12 + z + -7z] = 3(z + 2) Combine like terms: z + -7z = -6z 2[-12 + -6z] = 3(z + 2) [-12 * 2 + -6z * 2] = 3(z + 2) [-24 + -12z] = 3(z + 2) Reorder the terms: -24 + -12z = 3(2 + z) -24 + -12z = (2 * 3 + z * 3) -24 + -12z = (6 + 3z) Solving -24 + -12z = 6 + 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. -24 + -12z + -3z = 6 + 3z + -3z Combine like terms: -12z + -3z = -15z -24 + -15z = 6 + 3z + -3z Combine like terms: 3z + -3z = 0 -24 + -15z = 6 + 0 -24 + -15z = 6 Add '24' to each side of the equation. -24 + 24 + -15z = 6 + 24 Combine like terms: -24 + 24 = 0 0 + -15z = 6 + 24 -15z = 6 + 24 Combine like terms: 6 + 24 = 30 -15z = 30 Divide each side by '-15'. z = -2 Simplifying z = -2
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