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Simplifying 5(2z + -1) + -2(z + 5) = 5(z + 1) Reorder the terms: 5(-1 + 2z) + -2(z + 5) = 5(z + 1) (-1 * 5 + 2z * 5) + -2(z + 5) = 5(z + 1) (-5 + 10z) + -2(z + 5) = 5(z + 1) Reorder the terms: -5 + 10z + -2(5 + z) = 5(z + 1) -5 + 10z + (5 * -2 + z * -2) = 5(z + 1) -5 + 10z + (-10 + -2z) = 5(z + 1) Reorder the terms: -5 + -10 + 10z + -2z = 5(z + 1) Combine like terms: -5 + -10 = -15 -15 + 10z + -2z = 5(z + 1) Combine like terms: 10z + -2z = 8z -15 + 8z = 5(z + 1) Reorder the terms: -15 + 8z = 5(1 + z) -15 + 8z = (1 * 5 + z * 5) -15 + 8z = (5 + 5z) Solving -15 + 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. -15 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -15 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -15 + 3z = 5 + 0 -15 + 3z = 5 Add '15' to each side of the equation. -15 + 15 + 3z = 5 + 15 Combine like terms: -15 + 15 = 0 0 + 3z = 5 + 15 3z = 5 + 15 Combine like terms: 5 + 15 = 20 3z = 20 Divide each side by '3'. z = 6.666666667 Simplifying z = 6.666666667
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