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Simplifying 5(4z + -1) + -2(z + 3) = 5(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 3) = 5(z + 1) (-1 * 5 + 4z * 5) + -2(z + 3) = 5(z + 1) (-5 + 20z) + -2(z + 3) = 5(z + 1) Reorder the terms: -5 + 20z + -2(3 + z) = 5(z + 1) -5 + 20z + (3 * -2 + z * -2) = 5(z + 1) -5 + 20z + (-6 + -2z) = 5(z + 1) Reorder the terms: -5 + -6 + 20z + -2z = 5(z + 1) Combine like terms: -5 + -6 = -11 -11 + 20z + -2z = 5(z + 1) Combine like terms: 20z + -2z = 18z -11 + 18z = 5(z + 1) Reorder the terms: -11 + 18z = 5(1 + z) -11 + 18z = (1 * 5 + z * 5) -11 + 18z = (5 + 5z) Solving -11 + 18z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -11 + 18z + -5z = 5 + 5z + -5z Combine like terms: 18z + -5z = 13z -11 + 13z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -11 + 13z = 5 + 0 -11 + 13z = 5 Add '11' to each side of the equation. -11 + 11 + 13z = 5 + 11 Combine like terms: -11 + 11 = 0 0 + 13z = 5 + 11 13z = 5 + 11 Combine like terms: 5 + 11 = 16 13z = 16 Divide each side by '13'. z = 1.230769231 Simplifying z = 1.230769231
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