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Simplifying 5(8z + -1) + -7(4z + 1) + 8(7 + -4z) = 9 Reorder the terms: 5(-1 + 8z) + -7(4z + 1) + 8(7 + -4z) = 9 (-1 * 5 + 8z * 5) + -7(4z + 1) + 8(7 + -4z) = 9 (-5 + 40z) + -7(4z + 1) + 8(7 + -4z) = 9 Reorder the terms: -5 + 40z + -7(1 + 4z) + 8(7 + -4z) = 9 -5 + 40z + (1 * -7 + 4z * -7) + 8(7 + -4z) = 9 -5 + 40z + (-7 + -28z) + 8(7 + -4z) = 9 -5 + 40z + -7 + -28z + (7 * 8 + -4z * 8) = 9 -5 + 40z + -7 + -28z + (56 + -32z) = 9 Reorder the terms: -5 + -7 + 56 + 40z + -28z + -32z = 9 Combine like terms: -5 + -7 = -12 -12 + 56 + 40z + -28z + -32z = 9 Combine like terms: -12 + 56 = 44 44 + 40z + -28z + -32z = 9 Combine like terms: 40z + -28z = 12z 44 + 12z + -32z = 9 Combine like terms: 12z + -32z = -20z 44 + -20z = 9 Solving 44 + -20z = 9 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + -20z = 9 + -44 Combine like terms: 44 + -44 = 0 0 + -20z = 9 + -44 -20z = 9 + -44 Combine like terms: 9 + -44 = -35 -20z = -35 Divide each side by '-20'. z = 1.75 Simplifying z = 1.75
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