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Simplifying 5[1 + -2(2z + -1)] = -3(3z + -1) + 1 Reorder the terms: 5[1 + -2(-1 + 2z)] = -3(3z + -1) + 1 5[1 + (-1 * -2 + 2z * -2)] = -3(3z + -1) + 1 5[1 + (2 + -4z)] = -3(3z + -1) + 1 Combine like terms: 1 + 2 = 3 5[3 + -4z] = -3(3z + -1) + 1 [3 * 5 + -4z * 5] = -3(3z + -1) + 1 [15 + -20z] = -3(3z + -1) + 1 Reorder the terms: 15 + -20z = -3(-1 + 3z) + 1 15 + -20z = (-1 * -3 + 3z * -3) + 1 15 + -20z = (3 + -9z) + 1 Reorder the terms: 15 + -20z = 3 + 1 + -9z Combine like terms: 3 + 1 = 4 15 + -20z = 4 + -9z Solving 15 + -20z = 4 + -9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9z' to each side of the equation. 15 + -20z + 9z = 4 + -9z + 9z Combine like terms: -20z + 9z = -11z 15 + -11z = 4 + -9z + 9z Combine like terms: -9z + 9z = 0 15 + -11z = 4 + 0 15 + -11z = 4 Add '-15' to each side of the equation. 15 + -15 + -11z = 4 + -15 Combine like terms: 15 + -15 = 0 0 + -11z = 4 + -15 -11z = 4 + -15 Combine like terms: 4 + -15 = -11 -11z = -11 Divide each side by '-11'. z = 1 Simplifying z = 1
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