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Simplifying 5[1 + -2(2z + -1)] = -3(32 + -1) + 1 Reorder the terms: 5[1 + -2(-1 + 2z)] = -3(32 + -1) + 1 5[1 + (-1 * -2 + 2z * -2)] = -3(32 + -1) + 1 5[1 + (2 + -4z)] = -3(32 + -1) + 1 Combine like terms: 1 + 2 = 3 5[3 + -4z] = -3(32 + -1) + 1 [3 * 5 + -4z * 5] = -3(32 + -1) + 1 [15 + -20z] = -3(32 + -1) + 1 Combine like terms: 32 + -1 = 31 15 + -20z = -3(31) + 1 Multiply -3 * 31 15 + -20z = -93 + 1 Combine like terms: -93 + 1 = -92 15 + -20z = -92 Solving 15 + -20z = -92 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -20z = -92 + -15 Combine like terms: 15 + -15 = 0 0 + -20z = -92 + -15 -20z = -92 + -15 Combine like terms: -92 + -15 = -107 -20z = -107 Divide each side by '-20'. z = 5.35 Simplifying z = 5.35
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