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Simplifying -10(z + 2) + 4(4z + -7) = 5(z + -6) + 8 Reorder the terms: -10(2 + z) + 4(4z + -7) = 5(z + -6) + 8 (2 * -10 + z * -10) + 4(4z + -7) = 5(z + -6) + 8 (-20 + -10z) + 4(4z + -7) = 5(z + -6) + 8 Reorder the terms: -20 + -10z + 4(-7 + 4z) = 5(z + -6) + 8 -20 + -10z + (-7 * 4 + 4z * 4) = 5(z + -6) + 8 -20 + -10z + (-28 + 16z) = 5(z + -6) + 8 Reorder the terms: -20 + -28 + -10z + 16z = 5(z + -6) + 8 Combine like terms: -20 + -28 = -48 -48 + -10z + 16z = 5(z + -6) + 8 Combine like terms: -10z + 16z = 6z -48 + 6z = 5(z + -6) + 8 Reorder the terms: -48 + 6z = 5(-6 + z) + 8 -48 + 6z = (-6 * 5 + z * 5) + 8 -48 + 6z = (-30 + 5z) + 8 Reorder the terms: -48 + 6z = -30 + 8 + 5z Combine like terms: -30 + 8 = -22 -48 + 6z = -22 + 5z Solving -48 + 6z = -22 + 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. -48 + 6z + -5z = -22 + 5z + -5z Combine like terms: 6z + -5z = 1z -48 + 1z = -22 + 5z + -5z Combine like terms: 5z + -5z = 0 -48 + 1z = -22 + 0 -48 + 1z = -22 Add '48' to each side of the equation. -48 + 48 + 1z = -22 + 48 Combine like terms: -48 + 48 = 0 0 + 1z = -22 + 48 1z = -22 + 48 Combine like terms: -22 + 48 = 26 1z = 26 Divide each side by '1'. z = 26 Simplifying z = 26
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