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Simplifying 5(2z + -1) + -3(z + 2) = 2(z + 1) Reorder the terms: 5(-1 + 2z) + -3(z + 2) = 2(z + 1) (-1 * 5 + 2z * 5) + -3(z + 2) = 2(z + 1) (-5 + 10z) + -3(z + 2) = 2(z + 1) Reorder the terms: -5 + 10z + -3(2 + z) = 2(z + 1) -5 + 10z + (2 * -3 + z * -3) = 2(z + 1) -5 + 10z + (-6 + -3z) = 2(z + 1) Reorder the terms: -5 + -6 + 10z + -3z = 2(z + 1) Combine like terms: -5 + -6 = -11 -11 + 10z + -3z = 2(z + 1) Combine like terms: 10z + -3z = 7z -11 + 7z = 2(z + 1) Reorder the terms: -11 + 7z = 2(1 + z) -11 + 7z = (1 * 2 + z * 2) -11 + 7z = (2 + 2z) Solving -11 + 7z = 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. -11 + 7z + -2z = 2 + 2z + -2z Combine like terms: 7z + -2z = 5z -11 + 5z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -11 + 5z = 2 + 0 -11 + 5z = 2 Add '11' to each side of the equation. -11 + 11 + 5z = 2 + 11 Combine like terms: -11 + 11 = 0 0 + 5z = 2 + 11 5z = 2 + 11 Combine like terms: 2 + 11 = 13 5z = 13 Divide each side by '5'. z = 2.6 Simplifying z = 2.6
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