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Simplifying 5(3z + -1) + -2(z + 7) = 10(z + 1) Reorder the terms: 5(-1 + 3z) + -2(z + 7) = 10(z + 1) (-1 * 5 + 3z * 5) + -2(z + 7) = 10(z + 1) (-5 + 15z) + -2(z + 7) = 10(z + 1) Reorder the terms: -5 + 15z + -2(7 + z) = 10(z + 1) -5 + 15z + (7 * -2 + z * -2) = 10(z + 1) -5 + 15z + (-14 + -2z) = 10(z + 1) Reorder the terms: -5 + -14 + 15z + -2z = 10(z + 1) Combine like terms: -5 + -14 = -19 -19 + 15z + -2z = 10(z + 1) Combine like terms: 15z + -2z = 13z -19 + 13z = 10(z + 1) Reorder the terms: -19 + 13z = 10(1 + z) -19 + 13z = (1 * 10 + z * 10) -19 + 13z = (10 + 10z) Solving -19 + 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. -19 + 13z + -10z = 10 + 10z + -10z Combine like terms: 13z + -10z = 3z -19 + 3z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -19 + 3z = 10 + 0 -19 + 3z = 10 Add '19' to each side of the equation. -19 + 19 + 3z = 10 + 19 Combine like terms: -19 + 19 = 0 0 + 3z = 10 + 19 3z = 10 + 19 Combine like terms: 10 + 19 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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