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Simplifying 5(2z + -1) + -2(z + -9) = 5(z + 1) Reorder the terms: 5(-1 + 2z) + -2(z + -9) = 5(z + 1) (-1 * 5 + 2z * 5) + -2(z + -9) = 5(z + 1) (-5 + 10z) + -2(z + -9) = 5(z + 1) Reorder the terms: -5 + 10z + -2(-9 + z) = 5(z + 1) -5 + 10z + (-9 * -2 + z * -2) = 5(z + 1) -5 + 10z + (18 + -2z) = 5(z + 1) Reorder the terms: -5 + 18 + 10z + -2z = 5(z + 1) Combine like terms: -5 + 18 = 13 13 + 10z + -2z = 5(z + 1) Combine like terms: 10z + -2z = 8z 13 + 8z = 5(z + 1) Reorder the terms: 13 + 8z = 5(1 + z) 13 + 8z = (1 * 5 + z * 5) 13 + 8z = (5 + 5z) Solving 13 + 8z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. 13 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z 13 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 13 + 3z = 5 + 0 13 + 3z = 5 Add '-13' to each side of the equation. 13 + -13 + 3z = 5 + -13 Combine like terms: 13 + -13 = 0 0 + 3z = 5 + -13 3z = 5 + -13 Combine like terms: 5 + -13 = -8 3z = -8 Divide each side by '3'. z = -2.666666667 Simplifying z = -2.666666667
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