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Simplifying 5(2z + -1) + -2(z + 2) = 2(z + 1) Reorder the terms: 5(-1 + 2z) + -2(z + 2) = 2(z + 1) (-1 * 5 + 2z * 5) + -2(z + 2) = 2(z + 1) (-5 + 10z) + -2(z + 2) = 2(z + 1) Reorder the terms: -5 + 10z + -2(2 + z) = 2(z + 1) -5 + 10z + (2 * -2 + z * -2) = 2(z + 1) -5 + 10z + (-4 + -2z) = 2(z + 1) Reorder the terms: -5 + -4 + 10z + -2z = 2(z + 1) Combine like terms: -5 + -4 = -9 -9 + 10z + -2z = 2(z + 1) Combine like terms: 10z + -2z = 8z -9 + 8z = 2(z + 1) Reorder the terms: -9 + 8z = 2(1 + z) -9 + 8z = (1 * 2 + z * 2) -9 + 8z = (2 + 2z) Solving -9 + 8z = 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. -9 + 8z + -2z = 2 + 2z + -2z Combine like terms: 8z + -2z = 6z -9 + 6z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -9 + 6z = 2 + 0 -9 + 6z = 2 Add '9' to each side of the equation. -9 + 9 + 6z = 2 + 9 Combine like terms: -9 + 9 = 0 0 + 6z = 2 + 9 6z = 2 + 9 Combine like terms: 2 + 9 = 11 6z = 11 Divide each side by '6'. z = 1.833333333 Simplifying z = 1.833333333
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