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Simplifying 5(4z + -1) + -3(z + 5) = 15(z + 1) Reorder the terms: 5(-1 + 4z) + -3(z + 5) = 15(z + 1) (-1 * 5 + 4z * 5) + -3(z + 5) = 15(z + 1) (-5 + 20z) + -3(z + 5) = 15(z + 1) Reorder the terms: -5 + 20z + -3(5 + z) = 15(z + 1) -5 + 20z + (5 * -3 + z * -3) = 15(z + 1) -5 + 20z + (-15 + -3z) = 15(z + 1) Reorder the terms: -5 + -15 + 20z + -3z = 15(z + 1) Combine like terms: -5 + -15 = -20 -20 + 20z + -3z = 15(z + 1) Combine like terms: 20z + -3z = 17z -20 + 17z = 15(z + 1) Reorder the terms: -20 + 17z = 15(1 + z) -20 + 17z = (1 * 15 + z * 15) -20 + 17z = (15 + 15z) Solving -20 + 17z = 15 + 15z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15z' to each side of the equation. -20 + 17z + -15z = 15 + 15z + -15z Combine like terms: 17z + -15z = 2z -20 + 2z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -20 + 2z = 15 + 0 -20 + 2z = 15 Add '20' to each side of the equation. -20 + 20 + 2z = 15 + 20 Combine like terms: -20 + 20 = 0 0 + 2z = 15 + 20 2z = 15 + 20 Combine like terms: 15 + 20 = 35 2z = 35 Divide each side by '2'. z = 17.5 Simplifying z = 17.5
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