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Simplifying 8(7 + -4z) + 5(8z + -1) = 7(4z + 1) + 19 (7 * 8 + -4z * 8) + 5(8z + -1) = 7(4z + 1) + 19 (56 + -32z) + 5(8z + -1) = 7(4z + 1) + 19 Reorder the terms: 56 + -32z + 5(-1 + 8z) = 7(4z + 1) + 19 56 + -32z + (-1 * 5 + 8z * 5) = 7(4z + 1) + 19 56 + -32z + (-5 + 40z) = 7(4z + 1) + 19 Reorder the terms: 56 + -5 + -32z + 40z = 7(4z + 1) + 19 Combine like terms: 56 + -5 = 51 51 + -32z + 40z = 7(4z + 1) + 19 Combine like terms: -32z + 40z = 8z 51 + 8z = 7(4z + 1) + 19 Reorder the terms: 51 + 8z = 7(1 + 4z) + 19 51 + 8z = (1 * 7 + 4z * 7) + 19 51 + 8z = (7 + 28z) + 19 Reorder the terms: 51 + 8z = 7 + 19 + 28z Combine like terms: 7 + 19 = 26 51 + 8z = 26 + 28z Solving 51 + 8z = 26 + 28z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-28z' to each side of the equation. 51 + 8z + -28z = 26 + 28z + -28z Combine like terms: 8z + -28z = -20z 51 + -20z = 26 + 28z + -28z Combine like terms: 28z + -28z = 0 51 + -20z = 26 + 0 51 + -20z = 26 Add '-51' to each side of the equation. 51 + -51 + -20z = 26 + -51 Combine like terms: 51 + -51 = 0 0 + -20z = 26 + -51 -20z = 26 + -51 Combine like terms: 26 + -51 = -25 -20z = -25 Divide each side by '-20'. z = 1.25 Simplifying z = 1.25
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