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Simplifying 5(4z + -1) + -2(z + 3) = 2(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 3) = 2(z + 1) (-1 * 5 + 4z * 5) + -2(z + 3) = 2(z + 1) (-5 + 20z) + -2(z + 3) = 2(z + 1) Reorder the terms: -5 + 20z + -2(3 + z) = 2(z + 1) -5 + 20z + (3 * -2 + z * -2) = 2(z + 1) -5 + 20z + (-6 + -2z) = 2(z + 1) Reorder the terms: -5 + -6 + 20z + -2z = 2(z + 1) Combine like terms: -5 + -6 = -11 -11 + 20z + -2z = 2(z + 1) Combine like terms: 20z + -2z = 18z -11 + 18z = 2(z + 1) Reorder the terms: -11 + 18z = 2(1 + z) -11 + 18z = (1 * 2 + z * 2) -11 + 18z = (2 + 2z) Solving -11 + 18z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -11 + 18z + -2z = 2 + 2z + -2z Combine like terms: 18z + -2z = 16z -11 + 16z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -11 + 16z = 2 + 0 -11 + 16z = 2 Add '11' to each side of the equation. -11 + 11 + 16z = 2 + 11 Combine like terms: -11 + 11 = 0 0 + 16z = 2 + 11 16z = 2 + 11 Combine like terms: 2 + 11 = 13 16z = 13 Divide each side by '16'. z = 0.8125 Simplifying z = 0.8125
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