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Simplifying 5(6z + -1) + -2(z + 1) = 15(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 1) = 15(z + 1) (-1 * 5 + 6z * 5) + -2(z + 1) = 15(z + 1) (-5 + 30z) + -2(z + 1) = 15(z + 1) Reorder the terms: -5 + 30z + -2(1 + z) = 15(z + 1) -5 + 30z + (1 * -2 + z * -2) = 15(z + 1) -5 + 30z + (-2 + -2z) = 15(z + 1) Reorder the terms: -5 + -2 + 30z + -2z = 15(z + 1) Combine like terms: -5 + -2 = -7 -7 + 30z + -2z = 15(z + 1) Combine like terms: 30z + -2z = 28z -7 + 28z = 15(z + 1) Reorder the terms: -7 + 28z = 15(1 + z) -7 + 28z = (1 * 15 + z * 15) -7 + 28z = (15 + 15z) Solving -7 + 28z = 15 + 15z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15z' to each side of the equation. -7 + 28z + -15z = 15 + 15z + -15z Combine like terms: 28z + -15z = 13z -7 + 13z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -7 + 13z = 15 + 0 -7 + 13z = 15 Add '7' to each side of the equation. -7 + 7 + 13z = 15 + 7 Combine like terms: -7 + 7 = 0 0 + 13z = 15 + 7 13z = 15 + 7 Combine like terms: 15 + 7 = 22 13z = 22 Divide each side by '13'. z = 1.692307692 Simplifying z = 1.692307692
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