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Simplifying 5(4z + -1) + -2(z + 7) = 14(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 7) = 14(z + 1) (-1 * 5 + 4z * 5) + -2(z + 7) = 14(z + 1) (-5 + 20z) + -2(z + 7) = 14(z + 1) Reorder the terms: -5 + 20z + -2(7 + z) = 14(z + 1) -5 + 20z + (7 * -2 + z * -2) = 14(z + 1) -5 + 20z + (-14 + -2z) = 14(z + 1) Reorder the terms: -5 + -14 + 20z + -2z = 14(z + 1) Combine like terms: -5 + -14 = -19 -19 + 20z + -2z = 14(z + 1) Combine like terms: 20z + -2z = 18z -19 + 18z = 14(z + 1) Reorder the terms: -19 + 18z = 14(1 + z) -19 + 18z = (1 * 14 + z * 14) -19 + 18z = (14 + 14z) Solving -19 + 18z = 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. -19 + 18z + -14z = 14 + 14z + -14z Combine like terms: 18z + -14z = 4z -19 + 4z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -19 + 4z = 14 + 0 -19 + 4z = 14 Add '19' to each side of the equation. -19 + 19 + 4z = 14 + 19 Combine like terms: -19 + 19 = 0 0 + 4z = 14 + 19 4z = 14 + 19 Combine like terms: 14 + 19 = 33 4z = 33 Divide each side by '4'. z = 8.25 Simplifying z = 8.25
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