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Simplifying -9(z + 3) + 4(4z + -5) = 6(z + -5) + 13 Reorder the terms: -9(3 + z) + 4(4z + -5) = 6(z + -5) + 13 (3 * -9 + z * -9) + 4(4z + -5) = 6(z + -5) + 13 (-27 + -9z) + 4(4z + -5) = 6(z + -5) + 13 Reorder the terms: -27 + -9z + 4(-5 + 4z) = 6(z + -5) + 13 -27 + -9z + (-5 * 4 + 4z * 4) = 6(z + -5) + 13 -27 + -9z + (-20 + 16z) = 6(z + -5) + 13 Reorder the terms: -27 + -20 + -9z + 16z = 6(z + -5) + 13 Combine like terms: -27 + -20 = -47 -47 + -9z + 16z = 6(z + -5) + 13 Combine like terms: -9z + 16z = 7z -47 + 7z = 6(z + -5) + 13 Reorder the terms: -47 + 7z = 6(-5 + z) + 13 -47 + 7z = (-5 * 6 + z * 6) + 13 -47 + 7z = (-30 + 6z) + 13 Reorder the terms: -47 + 7z = -30 + 13 + 6z Combine like terms: -30 + 13 = -17 -47 + 7z = -17 + 6z Solving -47 + 7z = -17 + 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. -47 + 7z + -6z = -17 + 6z + -6z Combine like terms: 7z + -6z = 1z -47 + 1z = -17 + 6z + -6z Combine like terms: 6z + -6z = 0 -47 + 1z = -17 + 0 -47 + 1z = -17 Add '47' to each side of the equation. -47 + 47 + 1z = -17 + 47 Combine like terms: -47 + 47 = 0 0 + 1z = -17 + 47 1z = -17 + 47 Combine like terms: -17 + 47 = 30 1z = 30 Divide each side by '1'. z = 30 Simplifying z = 30
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