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Simplifying -14(z + 1) + 5(4z + -7) = 5(z + -5) + 13 Reorder the terms: -14(1 + z) + 5(4z + -7) = 5(z + -5) + 13 (1 * -14 + z * -14) + 5(4z + -7) = 5(z + -5) + 13 (-14 + -14z) + 5(4z + -7) = 5(z + -5) + 13 Reorder the terms: -14 + -14z + 5(-7 + 4z) = 5(z + -5) + 13 -14 + -14z + (-7 * 5 + 4z * 5) = 5(z + -5) + 13 -14 + -14z + (-35 + 20z) = 5(z + -5) + 13 Reorder the terms: -14 + -35 + -14z + 20z = 5(z + -5) + 13 Combine like terms: -14 + -35 = -49 -49 + -14z + 20z = 5(z + -5) + 13 Combine like terms: -14z + 20z = 6z -49 + 6z = 5(z + -5) + 13 Reorder the terms: -49 + 6z = 5(-5 + z) + 13 -49 + 6z = (-5 * 5 + z * 5) + 13 -49 + 6z = (-25 + 5z) + 13 Reorder the terms: -49 + 6z = -25 + 13 + 5z Combine like terms: -25 + 13 = -12 -49 + 6z = -12 + 5z Solving -49 + 6z = -12 + 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. -49 + 6z + -5z = -12 + 5z + -5z Combine like terms: 6z + -5z = 1z -49 + 1z = -12 + 5z + -5z Combine like terms: 5z + -5z = 0 -49 + 1z = -12 + 0 -49 + 1z = -12 Add '49' to each side of the equation. -49 + 49 + 1z = -12 + 49 Combine like terms: -49 + 49 = 0 0 + 1z = -12 + 49 1z = -12 + 49 Combine like terms: -12 + 49 = 37 1z = 37 Divide each side by '1'. z = 37 Simplifying z = 37
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