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Simplifying 3(4z + -1) + -2(z + 2) = 4(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 2) = 4(z + 1) (-1 * 3 + 4z * 3) + -2(z + 2) = 4(z + 1) (-3 + 12z) + -2(z + 2) = 4(z + 1) Reorder the terms: -3 + 12z + -2(2 + z) = 4(z + 1) -3 + 12z + (2 * -2 + z * -2) = 4(z + 1) -3 + 12z + (-4 + -2z) = 4(z + 1) Reorder the terms: -3 + -4 + 12z + -2z = 4(z + 1) Combine like terms: -3 + -4 = -7 -7 + 12z + -2z = 4(z + 1) Combine like terms: 12z + -2z = 10z -7 + 10z = 4(z + 1) Reorder the terms: -7 + 10z = 4(1 + z) -7 + 10z = (1 * 4 + z * 4) -7 + 10z = (4 + 4z) Solving -7 + 10z = 4 + 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. -7 + 10z + -4z = 4 + 4z + -4z Combine like terms: 10z + -4z = 6z -7 + 6z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -7 + 6z = 4 + 0 -7 + 6z = 4 Add '7' to each side of the equation. -7 + 7 + 6z = 4 + 7 Combine like terms: -7 + 7 = 0 0 + 6z = 4 + 7 6z = 4 + 7 Combine like terms: 4 + 7 = 11 6z = 11 Divide each side by '6'. z = 1.833333333 Simplifying z = 1.833333333
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