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Simplifying 12z + 2(z + -3) = 7 + 5(2z + -1) Reorder the terms: 12z + 2(-3 + z) = 7 + 5(2z + -1) 12z + (-3 * 2 + z * 2) = 7 + 5(2z + -1) 12z + (-6 + 2z) = 7 + 5(2z + -1) Reorder the terms: -6 + 12z + 2z = 7 + 5(2z + -1) Combine like terms: 12z + 2z = 14z -6 + 14z = 7 + 5(2z + -1) Reorder the terms: -6 + 14z = 7 + 5(-1 + 2z) -6 + 14z = 7 + (-1 * 5 + 2z * 5) -6 + 14z = 7 + (-5 + 10z) Combine like terms: 7 + -5 = 2 -6 + 14z = 2 + 10z Solving -6 + 14z = 2 + 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. -6 + 14z + -10z = 2 + 10z + -10z Combine like terms: 14z + -10z = 4z -6 + 4z = 2 + 10z + -10z Combine like terms: 10z + -10z = 0 -6 + 4z = 2 + 0 -6 + 4z = 2 Add '6' to each side of the equation. -6 + 6 + 4z = 2 + 6 Combine like terms: -6 + 6 = 0 0 + 4z = 2 + 6 4z = 2 + 6 Combine like terms: 2 + 6 = 8 4z = 8 Divide each side by '4'. z = 2 Simplifying z = 2
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