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Simplifying 5(2z + -1) + -3(z + 9) = 3(z + 1) Reorder the terms: 5(-1 + 2z) + -3(z + 9) = 3(z + 1) (-1 * 5 + 2z * 5) + -3(z + 9) = 3(z + 1) (-5 + 10z) + -3(z + 9) = 3(z + 1) Reorder the terms: -5 + 10z + -3(9 + z) = 3(z + 1) -5 + 10z + (9 * -3 + z * -3) = 3(z + 1) -5 + 10z + (-27 + -3z) = 3(z + 1) Reorder the terms: -5 + -27 + 10z + -3z = 3(z + 1) Combine like terms: -5 + -27 = -32 -32 + 10z + -3z = 3(z + 1) Combine like terms: 10z + -3z = 7z -32 + 7z = 3(z + 1) Reorder the terms: -32 + 7z = 3(1 + z) -32 + 7z = (1 * 3 + z * 3) -32 + 7z = (3 + 3z) Solving -32 + 7z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -32 + 7z + -3z = 3 + 3z + -3z Combine like terms: 7z + -3z = 4z -32 + 4z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -32 + 4z = 3 + 0 -32 + 4z = 3 Add '32' to each side of the equation. -32 + 32 + 4z = 3 + 32 Combine like terms: -32 + 32 = 0 0 + 4z = 3 + 32 4z = 3 + 32 Combine like terms: 3 + 32 = 35 4z = 35 Divide each side by '4'. z = 8.75 Simplifying z = 8.75
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