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Simplifying 5(4z + -1) + -2(Z + 2) = 14(Z + 1) Reorder the terms: 5(-1 + 4z) + -2(Z + 2) = 14(Z + 1) (-1 * 5 + 4z * 5) + -2(Z + 2) = 14(Z + 1) (-5 + 20z) + -2(Z + 2) = 14(Z + 1) Reorder the terms: -5 + 20z + -2(2 + Z) = 14(Z + 1) -5 + 20z + (2 * -2 + Z * -2) = 14(Z + 1) -5 + 20z + (-4 + -2Z) = 14(Z + 1) Reorder the terms: -5 + -4 + -2Z + 20z = 14(Z + 1) Combine like terms: -5 + -4 = -9 -9 + -2Z + 20z = 14(Z + 1) Reorder the terms: -9 + -2Z + 20z = 14(1 + Z) -9 + -2Z + 20z = (1 * 14 + Z * 14) -9 + -2Z + 20z = (14 + 14Z) Solving -9 + -2Z + 20z = 14 + 14Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-14Z' to each side of the equation. -9 + -2Z + -14Z + 20z = 14 + 14Z + -14Z Combine like terms: -2Z + -14Z = -16Z -9 + -16Z + 20z = 14 + 14Z + -14Z Combine like terms: 14Z + -14Z = 0 -9 + -16Z + 20z = 14 + 0 -9 + -16Z + 20z = 14 Add '9' to each side of the equation. -9 + -16Z + 9 + 20z = 14 + 9 Reorder the terms: -9 + 9 + -16Z + 20z = 14 + 9 Combine like terms: -9 + 9 = 0 0 + -16Z + 20z = 14 + 9 -16Z + 20z = 14 + 9 Combine like terms: 14 + 9 = 23 -16Z + 20z = 23 Add '-20z' to each side of the equation. -16Z + 20z + -20z = 23 + -20z Combine like terms: 20z + -20z = 0 -16Z + 0 = 23 + -20z -16Z = 23 + -20z Divide each side by '-16'. Z = -1.4375 + 1.25z Simplifying Z = -1.4375 + 1.25z
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