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Simplifying 5(3z + -1) + -2(z + 1) = 10(z + 1) Reorder the terms: 5(-1 + 3z) + -2(z + 1) = 10(z + 1) (-1 * 5 + 3z * 5) + -2(z + 1) = 10(z + 1) (-5 + 15z) + -2(z + 1) = 10(z + 1) Reorder the terms: -5 + 15z + -2(1 + z) = 10(z + 1) -5 + 15z + (1 * -2 + z * -2) = 10(z + 1) -5 + 15z + (-2 + -2z) = 10(z + 1) Reorder the terms: -5 + -2 + 15z + -2z = 10(z + 1) Combine like terms: -5 + -2 = -7 -7 + 15z + -2z = 10(z + 1) Combine like terms: 15z + -2z = 13z -7 + 13z = 10(z + 1) Reorder the terms: -7 + 13z = 10(1 + z) -7 + 13z = (1 * 10 + z * 10) -7 + 13z = (10 + 10z) Solving -7 + 13z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. -7 + 13z + -10z = 10 + 10z + -10z Combine like terms: 13z + -10z = 3z -7 + 3z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -7 + 3z = 10 + 0 -7 + 3z = 10 Add '7' to each side of the equation. -7 + 7 + 3z = 10 + 7 Combine like terms: -7 + 7 = 0 0 + 3z = 10 + 7 3z = 10 + 7 Combine like terms: 10 + 7 = 17 3z = 17 Divide each side by '3'. z = 5.666666667 Simplifying z = 5.666666667
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