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Simplifying 3(4z + -1) + -4(z + 2) = 4(z + 1) Reorder the terms: 3(-1 + 4z) + -4(z + 2) = 4(z + 1) (-1 * 3 + 4z * 3) + -4(z + 2) = 4(z + 1) (-3 + 12z) + -4(z + 2) = 4(z + 1) Reorder the terms: -3 + 12z + -4(2 + z) = 4(z + 1) -3 + 12z + (2 * -4 + z * -4) = 4(z + 1) -3 + 12z + (-8 + -4z) = 4(z + 1) Reorder the terms: -3 + -8 + 12z + -4z = 4(z + 1) Combine like terms: -3 + -8 = -11 -11 + 12z + -4z = 4(z + 1) Combine like terms: 12z + -4z = 8z -11 + 8z = 4(z + 1) Reorder the terms: -11 + 8z = 4(1 + z) -11 + 8z = (1 * 4 + z * 4) -11 + 8z = (4 + 4z) Solving -11 + 8z = 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. -11 + 8z + -4z = 4 + 4z + -4z Combine like terms: 8z + -4z = 4z -11 + 4z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -11 + 4z = 4 + 0 -11 + 4z = 4 Add '11' to each side of the equation. -11 + 11 + 4z = 4 + 11 Combine like terms: -11 + 11 = 0 0 + 4z = 4 + 11 4z = 4 + 11 Combine like terms: 4 + 11 = 15 4z = 15 Divide each side by '4'. z = 3.75 Simplifying z = 3.75
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