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Simplifying 4(5z + -1) + -3(z + 6) = 9(z + 1) Reorder the terms: 4(-1 + 5z) + -3(z + 6) = 9(z + 1) (-1 * 4 + 5z * 4) + -3(z + 6) = 9(z + 1) (-4 + 20z) + -3(z + 6) = 9(z + 1) Reorder the terms: -4 + 20z + -3(6 + z) = 9(z + 1) -4 + 20z + (6 * -3 + z * -3) = 9(z + 1) -4 + 20z + (-18 + -3z) = 9(z + 1) Reorder the terms: -4 + -18 + 20z + -3z = 9(z + 1) Combine like terms: -4 + -18 = -22 -22 + 20z + -3z = 9(z + 1) Combine like terms: 20z + -3z = 17z -22 + 17z = 9(z + 1) Reorder the terms: -22 + 17z = 9(1 + z) -22 + 17z = (1 * 9 + z * 9) -22 + 17z = (9 + 9z) Solving -22 + 17z = 9 + 9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9z' to each side of the equation. -22 + 17z + -9z = 9 + 9z + -9z Combine like terms: 17z + -9z = 8z -22 + 8z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -22 + 8z = 9 + 0 -22 + 8z = 9 Add '22' to each side of the equation. -22 + 22 + 8z = 9 + 22 Combine like terms: -22 + 22 = 0 0 + 8z = 9 + 22 8z = 9 + 22 Combine like terms: 9 + 22 = 31 8z = 31 Divide each side by '8'. z = 3.875 Simplifying z = 3.875
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