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Simplifying -8(z + 3) + 4(3z + -5) = 3(z + -6) + 8 Reorder the terms: -8(3 + z) + 4(3z + -5) = 3(z + -6) + 8 (3 * -8 + z * -8) + 4(3z + -5) = 3(z + -6) + 8 (-24 + -8z) + 4(3z + -5) = 3(z + -6) + 8 Reorder the terms: -24 + -8z + 4(-5 + 3z) = 3(z + -6) + 8 -24 + -8z + (-5 * 4 + 3z * 4) = 3(z + -6) + 8 -24 + -8z + (-20 + 12z) = 3(z + -6) + 8 Reorder the terms: -24 + -20 + -8z + 12z = 3(z + -6) + 8 Combine like terms: -24 + -20 = -44 -44 + -8z + 12z = 3(z + -6) + 8 Combine like terms: -8z + 12z = 4z -44 + 4z = 3(z + -6) + 8 Reorder the terms: -44 + 4z = 3(-6 + z) + 8 -44 + 4z = (-6 * 3 + z * 3) + 8 -44 + 4z = (-18 + 3z) + 8 Reorder the terms: -44 + 4z = -18 + 8 + 3z Combine like terms: -18 + 8 = -10 -44 + 4z = -10 + 3z Solving -44 + 4z = -10 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -44 + 4z + -3z = -10 + 3z + -3z Combine like terms: 4z + -3z = 1z -44 + 1z = -10 + 3z + -3z Combine like terms: 3z + -3z = 0 -44 + 1z = -10 + 0 -44 + 1z = -10 Add '44' to each side of the equation. -44 + 44 + 1z = -10 + 44 Combine like terms: -44 + 44 = 0 0 + 1z = -10 + 44 1z = -10 + 44 Combine like terms: -10 + 44 = 34 1z = 34 Divide each side by '1'. z = 34 Simplifying z = 34
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