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Simplifying (12z + -4) + -1(8 + 2z) = (2 + -3z) + -1(z + -12) Reorder the terms: (-4 + 12z) + -1(8 + 2z) = (2 + -3z) + -1(z + -12) Remove parenthesis around (-4 + 12z) -4 + 12z + -1(8 + 2z) = (2 + -3z) + -1(z + -12) -4 + 12z + (8 * -1 + 2z * -1) = (2 + -3z) + -1(z + -12) -4 + 12z + (-8 + -2z) = (2 + -3z) + -1(z + -12) Reorder the terms: -4 + -8 + 12z + -2z = (2 + -3z) + -1(z + -12) Combine like terms: -4 + -8 = -12 -12 + 12z + -2z = (2 + -3z) + -1(z + -12) Combine like terms: 12z + -2z = 10z -12 + 10z = (2 + -3z) + -1(z + -12) Remove parenthesis around (2 + -3z) -12 + 10z = 2 + -3z + -1(z + -12) Reorder the terms: -12 + 10z = 2 + -3z + -1(-12 + z) -12 + 10z = 2 + -3z + (-12 * -1 + z * -1) -12 + 10z = 2 + -3z + (12 + -1z) Reorder the terms: -12 + 10z = 2 + 12 + -3z + -1z Combine like terms: 2 + 12 = 14 -12 + 10z = 14 + -3z + -1z Combine like terms: -3z + -1z = -4z -12 + 10z = 14 + -4z Solving -12 + 10z = 14 + -4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4z' to each side of the equation. -12 + 10z + 4z = 14 + -4z + 4z Combine like terms: 10z + 4z = 14z -12 + 14z = 14 + -4z + 4z Combine like terms: -4z + 4z = 0 -12 + 14z = 14 + 0 -12 + 14z = 14 Add '12' to each side of the equation. -12 + 12 + 14z = 14 + 12 Combine like terms: -12 + 12 = 0 0 + 14z = 14 + 12 14z = 14 + 12 Combine like terms: 14 + 12 = 26 14z = 26 Divide each side by '14'. z = 1.857142857 Simplifying z = 1.857142857
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