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Simplifying 4(3z + -1) + -3(z + 2) = 3(z + 1) Reorder the terms: 4(-1 + 3z) + -3(z + 2) = 3(z + 1) (-1 * 4 + 3z * 4) + -3(z + 2) = 3(z + 1) (-4 + 12z) + -3(z + 2) = 3(z + 1) Reorder the terms: -4 + 12z + -3(2 + z) = 3(z + 1) -4 + 12z + (2 * -3 + z * -3) = 3(z + 1) -4 + 12z + (-6 + -3z) = 3(z + 1) Reorder the terms: -4 + -6 + 12z + -3z = 3(z + 1) Combine like terms: -4 + -6 = -10 -10 + 12z + -3z = 3(z + 1) Combine like terms: 12z + -3z = 9z -10 + 9z = 3(z + 1) Reorder the terms: -10 + 9z = 3(1 + z) -10 + 9z = (1 * 3 + z * 3) -10 + 9z = (3 + 3z) Solving -10 + 9z = 3 + 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 + 9z + -3z = 3 + 3z + -3z Combine like terms: 9z + -3z = 6z -10 + 6z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -10 + 6z = 3 + 0 -10 + 6z = 3 Add '10' to each side of the equation. -10 + 10 + 6z = 3 + 10 Combine like terms: -10 + 10 = 0 0 + 6z = 3 + 10 6z = 3 + 10 Combine like terms: 3 + 10 = 13 6z = 13 Divide each side by '6'. z = 2.166666667 Simplifying z = 2.166666667
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