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Simplifying 3z + -24(1 + -1z) = 5(1 + -2z) + -12 3z + (1 * -24 + -1z * -24) = 5(1 + -2z) + -12 3z + (-24 + 24z) = 5(1 + -2z) + -12 Reorder the terms: -24 + 3z + 24z = 5(1 + -2z) + -12 Combine like terms: 3z + 24z = 27z -24 + 27z = 5(1 + -2z) + -12 -24 + 27z = (1 * 5 + -2z * 5) + -12 -24 + 27z = (5 + -10z) + -12 Reorder the terms: -24 + 27z = 5 + -12 + -10z Combine like terms: 5 + -12 = -7 -24 + 27z = -7 + -10z Solving -24 + 27z = -7 + -10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10z' to each side of the equation. -24 + 27z + 10z = -7 + -10z + 10z Combine like terms: 27z + 10z = 37z -24 + 37z = -7 + -10z + 10z Combine like terms: -10z + 10z = 0 -24 + 37z = -7 + 0 -24 + 37z = -7 Add '24' to each side of the equation. -24 + 24 + 37z = -7 + 24 Combine like terms: -24 + 24 = 0 0 + 37z = -7 + 24 37z = -7 + 24 Combine like terms: -7 + 24 = 17 37z = 17 Divide each side by '37'. z = 0.4594594595 Simplifying z = 0.4594594595
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