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Simplifying 5(3z + -1) + -3(z + 4) = 3(z + 4) Reorder the terms: 5(-1 + 3z) + -3(z + 4) = 3(z + 4) (-1 * 5 + 3z * 5) + -3(z + 4) = 3(z + 4) (-5 + 15z) + -3(z + 4) = 3(z + 4) Reorder the terms: -5 + 15z + -3(4 + z) = 3(z + 4) -5 + 15z + (4 * -3 + z * -3) = 3(z + 4) -5 + 15z + (-12 + -3z) = 3(z + 4) Reorder the terms: -5 + -12 + 15z + -3z = 3(z + 4) Combine like terms: -5 + -12 = -17 -17 + 15z + -3z = 3(z + 4) Combine like terms: 15z + -3z = 12z -17 + 12z = 3(z + 4) Reorder the terms: -17 + 12z = 3(4 + z) -17 + 12z = (4 * 3 + z * 3) -17 + 12z = (12 + 3z) Solving -17 + 12z = 12 + 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. -17 + 12z + -3z = 12 + 3z + -3z Combine like terms: 12z + -3z = 9z -17 + 9z = 12 + 3z + -3z Combine like terms: 3z + -3z = 0 -17 + 9z = 12 + 0 -17 + 9z = 12 Add '17' to each side of the equation. -17 + 17 + 9z = 12 + 17 Combine like terms: -17 + 17 = 0 0 + 9z = 12 + 17 9z = 12 + 17 Combine like terms: 12 + 17 = 29 9z = 29 Divide each side by '9'. z = 3.222222222 Simplifying z = 3.222222222
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