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Simplifying 3[z + -1(8z + 33) + 5] = 2(z + 4) Reorder the terms: 3[z + -1(33 + 8z) + 5] = 2(z + 4) 3[z + (33 * -1 + 8z * -1) + 5] = 2(z + 4) 3[z + (-33 + -8z) + 5] = 2(z + 4) Reorder the terms: 3[-33 + 5 + z + -8z] = 2(z + 4) Combine like terms: -33 + 5 = -28 3[-28 + z + -8z] = 2(z + 4) Combine like terms: z + -8z = -7z 3[-28 + -7z] = 2(z + 4) [-28 * 3 + -7z * 3] = 2(z + 4) [-84 + -21z] = 2(z + 4) Reorder the terms: -84 + -21z = 2(4 + z) -84 + -21z = (4 * 2 + z * 2) -84 + -21z = (8 + 2z) Solving -84 + -21z = 8 + 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. -84 + -21z + -2z = 8 + 2z + -2z Combine like terms: -21z + -2z = -23z -84 + -23z = 8 + 2z + -2z Combine like terms: 2z + -2z = 0 -84 + -23z = 8 + 0 -84 + -23z = 8 Add '84' to each side of the equation. -84 + 84 + -23z = 8 + 84 Combine like terms: -84 + 84 = 0 0 + -23z = 8 + 84 -23z = 8 + 84 Combine like terms: 8 + 84 = 92 -23z = 92 Divide each side by '-23'. z = -4 Simplifying z = -4
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