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Simplifying 4(3z + -1) + -3(z + 4) = 5(z + 1) Reorder the terms: 4(-1 + 3z) + -3(z + 4) = 5(z + 1) (-1 * 4 + 3z * 4) + -3(z + 4) = 5(z + 1) (-4 + 12z) + -3(z + 4) = 5(z + 1) Reorder the terms: -4 + 12z + -3(4 + z) = 5(z + 1) -4 + 12z + (4 * -3 + z * -3) = 5(z + 1) -4 + 12z + (-12 + -3z) = 5(z + 1) Reorder the terms: -4 + -12 + 12z + -3z = 5(z + 1) Combine like terms: -4 + -12 = -16 -16 + 12z + -3z = 5(z + 1) Combine like terms: 12z + -3z = 9z -16 + 9z = 5(z + 1) Reorder the terms: -16 + 9z = 5(1 + z) -16 + 9z = (1 * 5 + z * 5) -16 + 9z = (5 + 5z) Solving -16 + 9z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -16 + 9z + -5z = 5 + 5z + -5z Combine like terms: 9z + -5z = 4z -16 + 4z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -16 + 4z = 5 + 0 -16 + 4z = 5 Add '16' to each side of the equation. -16 + 16 + 4z = 5 + 16 Combine like terms: -16 + 16 = 0 0 + 4z = 5 + 16 4z = 5 + 16 Combine like terms: 5 + 16 = 21 4z = 21 Divide each side by '4'. z = 5.25 Simplifying z = 5.25
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