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Simplifying 4(3z + -1) + -4(z + 2) = 5(z + 1) Reorder the terms: 4(-1 + 3z) + -4(z + 2) = 5(z + 1) (-1 * 4 + 3z * 4) + -4(z + 2) = 5(z + 1) (-4 + 12z) + -4(z + 2) = 5(z + 1) Reorder the terms: -4 + 12z + -4(2 + z) = 5(z + 1) -4 + 12z + (2 * -4 + z * -4) = 5(z + 1) -4 + 12z + (-8 + -4z) = 5(z + 1) Reorder the terms: -4 + -8 + 12z + -4z = 5(z + 1) Combine like terms: -4 + -8 = -12 -12 + 12z + -4z = 5(z + 1) Combine like terms: 12z + -4z = 8z -12 + 8z = 5(z + 1) Reorder the terms: -12 + 8z = 5(1 + z) -12 + 8z = (1 * 5 + z * 5) -12 + 8z = (5 + 5z) Solving -12 + 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. -12 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -12 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -12 + 3z = 5 + 0 -12 + 3z = 5 Add '12' to each side of the equation. -12 + 12 + 3z = 5 + 12 Combine like terms: -12 + 12 = 0 0 + 3z = 5 + 12 3z = 5 + 12 Combine like terms: 5 + 12 = 17 3z = 17 Divide each side by '3'. z = 5.666666667 Simplifying z = 5.666666667
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