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Simplifying 4(3z + -1) + -4(z + 7) = 5(z + 1) Reorder the terms: 4(-1 + 3z) + -4(z + 7) = 5(z + 1) (-1 * 4 + 3z * 4) + -4(z + 7) = 5(z + 1) (-4 + 12z) + -4(z + 7) = 5(z + 1) Reorder the terms: -4 + 12z + -4(7 + z) = 5(z + 1) -4 + 12z + (7 * -4 + z * -4) = 5(z + 1) -4 + 12z + (-28 + -4z) = 5(z + 1) Reorder the terms: -4 + -28 + 12z + -4z = 5(z + 1) Combine like terms: -4 + -28 = -32 -32 + 12z + -4z = 5(z + 1) Combine like terms: 12z + -4z = 8z -32 + 8z = 5(z + 1) Reorder the terms: -32 + 8z = 5(1 + z) -32 + 8z = (1 * 5 + z * 5) -32 + 8z = (5 + 5z) Solving -32 + 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. -32 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -32 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -32 + 3z = 5 + 0 -32 + 3z = 5 Add '32' to each side of the equation. -32 + 32 + 3z = 5 + 32 Combine like terms: -32 + 32 = 0 0 + 3z = 5 + 32 3z = 5 + 32 Combine like terms: 5 + 32 = 37 3z = 37 Divide each side by '3'. z = 12.33333333 Simplifying z = 12.33333333
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