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Simplifying 4(3z + -1) + -4(z + 5) = 5(z + 1) Reorder the terms: 4(-1 + 3z) + -4(z + 5) = 5(z + 1) (-1 * 4 + 3z * 4) + -4(z + 5) = 5(z + 1) (-4 + 12z) + -4(z + 5) = 5(z + 1) Reorder the terms: -4 + 12z + -4(5 + z) = 5(z + 1) -4 + 12z + (5 * -4 + z * -4) = 5(z + 1) -4 + 12z + (-20 + -4z) = 5(z + 1) Reorder the terms: -4 + -20 + 12z + -4z = 5(z + 1) Combine like terms: -4 + -20 = -24 -24 + 12z + -4z = 5(z + 1) Combine like terms: 12z + -4z = 8z -24 + 8z = 5(z + 1) Reorder the terms: -24 + 8z = 5(1 + z) -24 + 8z = (1 * 5 + z * 5) -24 + 8z = (5 + 5z) Solving -24 + 8z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -24 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -24 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -24 + 3z = 5 + 0 -24 + 3z = 5 Add '24' to each side of the equation. -24 + 24 + 3z = 5 + 24 Combine like terms: -24 + 24 = 0 0 + 3z = 5 + 24 3z = 5 + 24 Combine like terms: 5 + 24 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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