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Simplifying 4(3z + -1) + -5(z + 8) = 3(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 8) = 3(z + 1) (-1 * 4 + 3z * 4) + -5(z + 8) = 3(z + 1) (-4 + 12z) + -5(z + 8) = 3(z + 1) Reorder the terms: -4 + 12z + -5(8 + z) = 3(z + 1) -4 + 12z + (8 * -5 + z * -5) = 3(z + 1) -4 + 12z + (-40 + -5z) = 3(z + 1) Reorder the terms: -4 + -40 + 12z + -5z = 3(z + 1) Combine like terms: -4 + -40 = -44 -44 + 12z + -5z = 3(z + 1) Combine like terms: 12z + -5z = 7z -44 + 7z = 3(z + 1) Reorder the terms: -44 + 7z = 3(1 + z) -44 + 7z = (1 * 3 + z * 3) -44 + 7z = (3 + 3z) Solving -44 + 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. -44 + 7z + -3z = 3 + 3z + -3z Combine like terms: 7z + -3z = 4z -44 + 4z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -44 + 4z = 3 + 0 -44 + 4z = 3 Add '44' to each side of the equation. -44 + 44 + 4z = 3 + 44 Combine like terms: -44 + 44 = 0 0 + 4z = 3 + 44 4z = 3 + 44 Combine like terms: 3 + 44 = 47 4z = 47 Divide each side by '4'. z = 11.75 Simplifying z = 11.75
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