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Simplifying 4(5z + -1) + -3(z + 2) = 15(z + 1) Reorder the terms: 4(-1 + 5z) + -3(z + 2) = 15(z + 1) (-1 * 4 + 5z * 4) + -3(z + 2) = 15(z + 1) (-4 + 20z) + -3(z + 2) = 15(z + 1) Reorder the terms: -4 + 20z + -3(2 + z) = 15(z + 1) -4 + 20z + (2 * -3 + z * -3) = 15(z + 1) -4 + 20z + (-6 + -3z) = 15(z + 1) Reorder the terms: -4 + -6 + 20z + -3z = 15(z + 1) Combine like terms: -4 + -6 = -10 -10 + 20z + -3z = 15(z + 1) Combine like terms: 20z + -3z = 17z -10 + 17z = 15(z + 1) Reorder the terms: -10 + 17z = 15(1 + z) -10 + 17z = (1 * 15 + z * 15) -10 + 17z = (15 + 15z) Solving -10 + 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. -10 + 17z + -15z = 15 + 15z + -15z Combine like terms: 17z + -15z = 2z -10 + 2z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -10 + 2z = 15 + 0 -10 + 2z = 15 Add '10' to each side of the equation. -10 + 10 + 2z = 15 + 10 Combine like terms: -10 + 10 = 0 0 + 2z = 15 + 10 2z = 15 + 10 Combine like terms: 15 + 10 = 25 2z = 25 Divide each side by '2'. z = 12.5 Simplifying z = 12.5
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