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Simplifying 3(4z + -1) + -3(z + 4) = 4(z + 1) Reorder the terms: 3(-1 + 4z) + -3(z + 4) = 4(z + 1) (-1 * 3 + 4z * 3) + -3(z + 4) = 4(z + 1) (-3 + 12z) + -3(z + 4) = 4(z + 1) Reorder the terms: -3 + 12z + -3(4 + z) = 4(z + 1) -3 + 12z + (4 * -3 + z * -3) = 4(z + 1) -3 + 12z + (-12 + -3z) = 4(z + 1) Reorder the terms: -3 + -12 + 12z + -3z = 4(z + 1) Combine like terms: -3 + -12 = -15 -15 + 12z + -3z = 4(z + 1) Combine like terms: 12z + -3z = 9z -15 + 9z = 4(z + 1) Reorder the terms: -15 + 9z = 4(1 + z) -15 + 9z = (1 * 4 + z * 4) -15 + 9z = (4 + 4z) Solving -15 + 9z = 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. -15 + 9z + -4z = 4 + 4z + -4z Combine like terms: 9z + -4z = 5z -15 + 5z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -15 + 5z = 4 + 0 -15 + 5z = 4 Add '15' to each side of the equation. -15 + 15 + 5z = 4 + 15 Combine like terms: -15 + 15 = 0 0 + 5z = 4 + 15 5z = 4 + 15 Combine like terms: 4 + 15 = 19 5z = 19 Divide each side by '5'. z = 3.8 Simplifying z = 3.8
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