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Simplifying -13(z + 1) + 5(4z + -6) = 6(z + -5) + 9 Reorder the terms: -13(1 + z) + 5(4z + -6) = 6(z + -5) + 9 (1 * -13 + z * -13) + 5(4z + -6) = 6(z + -5) + 9 (-13 + -13z) + 5(4z + -6) = 6(z + -5) + 9 Reorder the terms: -13 + -13z + 5(-6 + 4z) = 6(z + -5) + 9 -13 + -13z + (-6 * 5 + 4z * 5) = 6(z + -5) + 9 -13 + -13z + (-30 + 20z) = 6(z + -5) + 9 Reorder the terms: -13 + -30 + -13z + 20z = 6(z + -5) + 9 Combine like terms: -13 + -30 = -43 -43 + -13z + 20z = 6(z + -5) + 9 Combine like terms: -13z + 20z = 7z -43 + 7z = 6(z + -5) + 9 Reorder the terms: -43 + 7z = 6(-5 + z) + 9 -43 + 7z = (-5 * 6 + z * 6) + 9 -43 + 7z = (-30 + 6z) + 9 Reorder the terms: -43 + 7z = -30 + 9 + 6z Combine like terms: -30 + 9 = -21 -43 + 7z = -21 + 6z Solving -43 + 7z = -21 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -43 + 7z + -6z = -21 + 6z + -6z Combine like terms: 7z + -6z = 1z -43 + 1z = -21 + 6z + -6z Combine like terms: 6z + -6z = 0 -43 + 1z = -21 + 0 -43 + 1z = -21 Add '43' to each side of the equation. -43 + 43 + 1z = -21 + 43 Combine like terms: -43 + 43 = 0 0 + 1z = -21 + 43 1z = -21 + 43 Combine like terms: -21 + 43 = 22 1z = 22 Divide each side by '1'. z = 22 Simplifying z = 22
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