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Simplifying -11(z + 3) + 4(4z + -7) = 4(z + -5) + 12 Reorder the terms: -11(3 + z) + 4(4z + -7) = 4(z + -5) + 12 (3 * -11 + z * -11) + 4(4z + -7) = 4(z + -5) + 12 (-33 + -11z) + 4(4z + -7) = 4(z + -5) + 12 Reorder the terms: -33 + -11z + 4(-7 + 4z) = 4(z + -5) + 12 -33 + -11z + (-7 * 4 + 4z * 4) = 4(z + -5) + 12 -33 + -11z + (-28 + 16z) = 4(z + -5) + 12 Reorder the terms: -33 + -28 + -11z + 16z = 4(z + -5) + 12 Combine like terms: -33 + -28 = -61 -61 + -11z + 16z = 4(z + -5) + 12 Combine like terms: -11z + 16z = 5z -61 + 5z = 4(z + -5) + 12 Reorder the terms: -61 + 5z = 4(-5 + z) + 12 -61 + 5z = (-5 * 4 + z * 4) + 12 -61 + 5z = (-20 + 4z) + 12 Reorder the terms: -61 + 5z = -20 + 12 + 4z Combine like terms: -20 + 12 = -8 -61 + 5z = -8 + 4z Solving -61 + 5z = -8 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -61 + 5z + -4z = -8 + 4z + -4z Combine like terms: 5z + -4z = 1z -61 + 1z = -8 + 4z + -4z Combine like terms: 4z + -4z = 0 -61 + 1z = -8 + 0 -61 + 1z = -8 Add '61' to each side of the equation. -61 + 61 + 1z = -8 + 61 Combine like terms: -61 + 61 = 0 0 + 1z = -8 + 61 1z = -8 + 61 Combine like terms: -8 + 61 = 53 1z = 53 Divide each side by '1'. z = 53 Simplifying z = 53
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