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Simplifying 5(2z + -1) + -5(z + 8) = 2(z + 1) Reorder the terms: 5(-1 + 2z) + -5(z + 8) = 2(z + 1) (-1 * 5 + 2z * 5) + -5(z + 8) = 2(z + 1) (-5 + 10z) + -5(z + 8) = 2(z + 1) Reorder the terms: -5 + 10z + -5(8 + z) = 2(z + 1) -5 + 10z + (8 * -5 + z * -5) = 2(z + 1) -5 + 10z + (-40 + -5z) = 2(z + 1) Reorder the terms: -5 + -40 + 10z + -5z = 2(z + 1) Combine like terms: -5 + -40 = -45 -45 + 10z + -5z = 2(z + 1) Combine like terms: 10z + -5z = 5z -45 + 5z = 2(z + 1) Reorder the terms: -45 + 5z = 2(1 + z) -45 + 5z = (1 * 2 + z * 2) -45 + 5z = (2 + 2z) Solving -45 + 5z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -45 + 5z + -2z = 2 + 2z + -2z Combine like terms: 5z + -2z = 3z -45 + 3z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -45 + 3z = 2 + 0 -45 + 3z = 2 Add '45' to each side of the equation. -45 + 45 + 3z = 2 + 45 Combine like terms: -45 + 45 = 0 0 + 3z = 2 + 45 3z = 2 + 45 Combine like terms: 2 + 45 = 47 3z = 47 Divide each side by '3'. z = 15.66666667 Simplifying z = 15.66666667
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