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Simplifying 4(3z + -1) + -5(z + 6) = 4(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 6) = 4(z + 1) (-1 * 4 + 3z * 4) + -5(z + 6) = 4(z + 1) (-4 + 12z) + -5(z + 6) = 4(z + 1) Reorder the terms: -4 + 12z + -5(6 + z) = 4(z + 1) -4 + 12z + (6 * -5 + z * -5) = 4(z + 1) -4 + 12z + (-30 + -5z) = 4(z + 1) Reorder the terms: -4 + -30 + 12z + -5z = 4(z + 1) Combine like terms: -4 + -30 = -34 -34 + 12z + -5z = 4(z + 1) Combine like terms: 12z + -5z = 7z -34 + 7z = 4(z + 1) Reorder the terms: -34 + 7z = 4(1 + z) -34 + 7z = (1 * 4 + z * 4) -34 + 7z = (4 + 4z) Solving -34 + 7z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -34 + 7z + -4z = 4 + 4z + -4z Combine like terms: 7z + -4z = 3z -34 + 3z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -34 + 3z = 4 + 0 -34 + 3z = 4 Add '34' to each side of the equation. -34 + 34 + 3z = 4 + 34 Combine like terms: -34 + 34 = 0 0 + 3z = 4 + 34 3z = 4 + 34 Combine like terms: 4 + 34 = 38 3z = 38 Divide each side by '3'. z = 12.66666667 Simplifying z = 12.66666667
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