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Simplifying 4(3z + -2) + -2(z + 1) = 3(z + 2) + -1 Reorder the terms: 4(-2 + 3z) + -2(z + 1) = 3(z + 2) + -1 (-2 * 4 + 3z * 4) + -2(z + 1) = 3(z + 2) + -1 (-8 + 12z) + -2(z + 1) = 3(z + 2) + -1 Reorder the terms: -8 + 12z + -2(1 + z) = 3(z + 2) + -1 -8 + 12z + (1 * -2 + z * -2) = 3(z + 2) + -1 -8 + 12z + (-2 + -2z) = 3(z + 2) + -1 Reorder the terms: -8 + -2 + 12z + -2z = 3(z + 2) + -1 Combine like terms: -8 + -2 = -10 -10 + 12z + -2z = 3(z + 2) + -1 Combine like terms: 12z + -2z = 10z -10 + 10z = 3(z + 2) + -1 Reorder the terms: -10 + 10z = 3(2 + z) + -1 -10 + 10z = (2 * 3 + z * 3) + -1 -10 + 10z = (6 + 3z) + -1 Reorder the terms: -10 + 10z = 6 + -1 + 3z Combine like terms: 6 + -1 = 5 -10 + 10z = 5 + 3z Solving -10 + 10z = 5 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -10 + 10z + -3z = 5 + 3z + -3z Combine like terms: 10z + -3z = 7z -10 + 7z = 5 + 3z + -3z Combine like terms: 3z + -3z = 0 -10 + 7z = 5 + 0 -10 + 7z = 5 Add '10' to each side of the equation. -10 + 10 + 7z = 5 + 10 Combine like terms: -10 + 10 = 0 0 + 7z = 5 + 10 7z = 5 + 10 Combine like terms: 5 + 10 = 15 7z = 15 Divide each side by '7'. z = 2.142857143 Simplifying z = 2.142857143
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