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Simplifying 4(5z + -1) + -2(z + 5) = 15(z + 1) Reorder the terms: 4(-1 + 5z) + -2(z + 5) = 15(z + 1) (-1 * 4 + 5z * 4) + -2(z + 5) = 15(z + 1) (-4 + 20z) + -2(z + 5) = 15(z + 1) Reorder the terms: -4 + 20z + -2(5 + z) = 15(z + 1) -4 + 20z + (5 * -2 + z * -2) = 15(z + 1) -4 + 20z + (-10 + -2z) = 15(z + 1) Reorder the terms: -4 + -10 + 20z + -2z = 15(z + 1) Combine like terms: -4 + -10 = -14 -14 + 20z + -2z = 15(z + 1) Combine like terms: 20z + -2z = 18z -14 + 18z = 15(z + 1) Reorder the terms: -14 + 18z = 15(1 + z) -14 + 18z = (1 * 15 + z * 15) -14 + 18z = (15 + 15z) Solving -14 + 18z = 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. -14 + 18z + -15z = 15 + 15z + -15z Combine like terms: 18z + -15z = 3z -14 + 3z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -14 + 3z = 15 + 0 -14 + 3z = 15 Add '14' to each side of the equation. -14 + 14 + 3z = 15 + 14 Combine like terms: -14 + 14 = 0 0 + 3z = 15 + 14 3z = 15 + 14 Combine like terms: 15 + 14 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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