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Simplifying 7(6z + -1) + 3(2z + 1) + -5(12z + -7) = 23 Reorder the terms: 7(-1 + 6z) + 3(2z + 1) + -5(12z + -7) = 23 (-1 * 7 + 6z * 7) + 3(2z + 1) + -5(12z + -7) = 23 (-7 + 42z) + 3(2z + 1) + -5(12z + -7) = 23 Reorder the terms: -7 + 42z + 3(1 + 2z) + -5(12z + -7) = 23 -7 + 42z + (1 * 3 + 2z * 3) + -5(12z + -7) = 23 -7 + 42z + (3 + 6z) + -5(12z + -7) = 23 Reorder the terms: -7 + 42z + 3 + 6z + -5(-7 + 12z) = 23 -7 + 42z + 3 + 6z + (-7 * -5 + 12z * -5) = 23 -7 + 42z + 3 + 6z + (35 + -60z) = 23 Reorder the terms: -7 + 3 + 35 + 42z + 6z + -60z = 23 Combine like terms: -7 + 3 = -4 -4 + 35 + 42z + 6z + -60z = 23 Combine like terms: -4 + 35 = 31 31 + 42z + 6z + -60z = 23 Combine like terms: 42z + 6z = 48z 31 + 48z + -60z = 23 Combine like terms: 48z + -60z = -12z 31 + -12z = 23 Solving 31 + -12z = 23 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -12z = 23 + -31 Combine like terms: 31 + -31 = 0 0 + -12z = 23 + -31 -12z = 23 + -31 Combine like terms: 23 + -31 = -8 -12z = -8 Divide each side by '-12'. z = 0.6666666667 Simplifying z = 0.6666666667
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