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Simplifying 5(4z + -1) + -2(z + 5) = 11(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 5) = 11(z + 1) (-1 * 5 + 4z * 5) + -2(z + 5) = 11(z + 1) (-5 + 20z) + -2(z + 5) = 11(z + 1) Reorder the terms: -5 + 20z + -2(5 + z) = 11(z + 1) -5 + 20z + (5 * -2 + z * -2) = 11(z + 1) -5 + 20z + (-10 + -2z) = 11(z + 1) Reorder the terms: -5 + -10 + 20z + -2z = 11(z + 1) Combine like terms: -5 + -10 = -15 -15 + 20z + -2z = 11(z + 1) Combine like terms: 20z + -2z = 18z -15 + 18z = 11(z + 1) Reorder the terms: -15 + 18z = 11(1 + z) -15 + 18z = (1 * 11 + z * 11) -15 + 18z = (11 + 11z) Solving -15 + 18z = 11 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. -15 + 18z + -11z = 11 + 11z + -11z Combine like terms: 18z + -11z = 7z -15 + 7z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -15 + 7z = 11 + 0 -15 + 7z = 11 Add '15' to each side of the equation. -15 + 15 + 7z = 11 + 15 Combine like terms: -15 + 15 = 0 0 + 7z = 11 + 15 7z = 11 + 15 Combine like terms: 11 + 15 = 26 7z = 26 Divide each side by '7'. z = 3.714285714 Simplifying z = 3.714285714
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