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Simplifying 4(5z + -1) + -5(z + 4) = 7(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 4) = 7(z + 1) (-1 * 4 + 5z * 4) + -5(z + 4) = 7(z + 1) (-4 + 20z) + -5(z + 4) = 7(z + 1) Reorder the terms: -4 + 20z + -5(4 + z) = 7(z + 1) -4 + 20z + (4 * -5 + z * -5) = 7(z + 1) -4 + 20z + (-20 + -5z) = 7(z + 1) Reorder the terms: -4 + -20 + 20z + -5z = 7(z + 1) Combine like terms: -4 + -20 = -24 -24 + 20z + -5z = 7(z + 1) Combine like terms: 20z + -5z = 15z -24 + 15z = 7(z + 1) Reorder the terms: -24 + 15z = 7(1 + z) -24 + 15z = (1 * 7 + z * 7) -24 + 15z = (7 + 7z) Solving -24 + 15z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -24 + 15z + -7z = 7 + 7z + -7z Combine like terms: 15z + -7z = 8z -24 + 8z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -24 + 8z = 7 + 0 -24 + 8z = 7 Add '24' to each side of the equation. -24 + 24 + 8z = 7 + 24 Combine like terms: -24 + 24 = 0 0 + 8z = 7 + 24 8z = 7 + 24 Combine like terms: 7 + 24 = 31 8z = 31 Divide each side by '8'. z = 3.875 Simplifying z = 3.875
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