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Simplifying 4(3z + -1) + -5(z + 2) = 3(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 2) = 3(z + 1) (-1 * 4 + 3z * 4) + -5(z + 2) = 3(z + 1) (-4 + 12z) + -5(z + 2) = 3(z + 1) Reorder the terms: -4 + 12z + -5(2 + z) = 3(z + 1) -4 + 12z + (2 * -5 + z * -5) = 3(z + 1) -4 + 12z + (-10 + -5z) = 3(z + 1) Reorder the terms: -4 + -10 + 12z + -5z = 3(z + 1) Combine like terms: -4 + -10 = -14 -14 + 12z + -5z = 3(z + 1) Combine like terms: 12z + -5z = 7z -14 + 7z = 3(z + 1) Reorder the terms: -14 + 7z = 3(1 + z) -14 + 7z = (1 * 3 + z * 3) -14 + 7z = (3 + 3z) Solving -14 + 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. -14 + 7z + -3z = 3 + 3z + -3z Combine like terms: 7z + -3z = 4z -14 + 4z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -14 + 4z = 3 + 0 -14 + 4z = 3 Add '14' to each side of the equation. -14 + 14 + 4z = 3 + 14 Combine like terms: -14 + 14 = 0 0 + 4z = 3 + 14 4z = 3 + 14 Combine like terms: 3 + 14 = 17 4z = 17 Divide each side by '4'. z = 4.25 Simplifying z = 4.25
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