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Simplifying -5(1 + -2z) + 4(3 + -1z) + -7(3 + 2) = 0 (1 * -5 + -2z * -5) + 4(3 + -1z) + -7(3 + 2) = 0 (-5 + 10z) + 4(3 + -1z) + -7(3 + 2) = 0 -5 + 10z + (3 * 4 + -1z * 4) + -7(3 + 2) = 0 -5 + 10z + (12 + -4z) + -7(3 + 2) = 0 Combine like terms: 3 + 2 = 5 -5 + 10z + 12 + -4z + -7(5) = 0 Multiply -7 * 5 -5 + 10z + 12 + -4z + -35 = 0 Reorder the terms: -5 + 12 + -35 + 10z + -4z = 0 Combine like terms: -5 + 12 = 7 7 + -35 + 10z + -4z = 0 Combine like terms: 7 + -35 = -28 -28 + 10z + -4z = 0 Combine like terms: 10z + -4z = 6z -28 + 6z = 0 Solving -28 + 6z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 6z = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 6z = 0 + 28 6z = 0 + 28 Combine like terms: 0 + 28 = 28 6z = 28 Divide each side by '6'. z = 4.666666667 Simplifying z = 4.666666667
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