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