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Simplifying 4(5z + -1) + -3(z + 6) = 15(z + 1) Reorder the terms: 4(-1 + 5z) + -3(z + 6) = 15(z + 1) (-1 * 4 + 5z * 4) + -3(z + 6) = 15(z + 1) (-4 + 20z) + -3(z + 6) = 15(z + 1) Reorder the terms: -4 + 20z + -3(6 + z) = 15(z + 1) -4 + 20z + (6 * -3 + z * -3) = 15(z + 1) -4 + 20z + (-18 + -3z) = 15(z + 1) Reorder the terms: -4 + -18 + 20z + -3z = 15(z + 1) Combine like terms: -4 + -18 = -22 -22 + 20z + -3z = 15(z + 1) Combine like terms: 20z + -3z = 17z -22 + 17z = 15(z + 1) Reorder the terms: -22 + 17z = 15(1 + z) -22 + 17z = (1 * 15 + z * 15) -22 + 17z = (15 + 15z) Solving -22 + 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. -22 + 17z + -15z = 15 + 15z + -15z Combine like terms: 17z + -15z = 2z -22 + 2z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -22 + 2z = 15 + 0 -22 + 2z = 15 Add '22' to each side of the equation. -22 + 22 + 2z = 15 + 22 Combine like terms: -22 + 22 = 0 0 + 2z = 15 + 22 2z = 15 + 22 Combine like terms: 15 + 22 = 37 2z = 37 Divide each side by '2'. z = 18.5 Simplifying z = 18.5
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