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Simplifying -11(z + 1) + 5(3z + -3) = 3(z + -5) + 13 Reorder the terms: -11(1 + z) + 5(3z + -3) = 3(z + -5) + 13 (1 * -11 + z * -11) + 5(3z + -3) = 3(z + -5) + 13 (-11 + -11z) + 5(3z + -3) = 3(z + -5) + 13 Reorder the terms: -11 + -11z + 5(-3 + 3z) = 3(z + -5) + 13 -11 + -11z + (-3 * 5 + 3z * 5) = 3(z + -5) + 13 -11 + -11z + (-15 + 15z) = 3(z + -5) + 13 Reorder the terms: -11 + -15 + -11z + 15z = 3(z + -5) + 13 Combine like terms: -11 + -15 = -26 -26 + -11z + 15z = 3(z + -5) + 13 Combine like terms: -11z + 15z = 4z -26 + 4z = 3(z + -5) + 13 Reorder the terms: -26 + 4z = 3(-5 + z) + 13 -26 + 4z = (-5 * 3 + z * 3) + 13 -26 + 4z = (-15 + 3z) + 13 Reorder the terms: -26 + 4z = -15 + 13 + 3z Combine like terms: -15 + 13 = -2 -26 + 4z = -2 + 3z Solving -26 + 4z = -2 + 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. -26 + 4z + -3z = -2 + 3z + -3z Combine like terms: 4z + -3z = 1z -26 + 1z = -2 + 3z + -3z Combine like terms: 3z + -3z = 0 -26 + 1z = -2 + 0 -26 + 1z = -2 Add '26' to each side of the equation. -26 + 26 + 1z = -2 + 26 Combine like terms: -26 + 26 = 0 0 + 1z = -2 + 26 1z = -2 + 26 Combine like terms: -2 + 26 = 24 1z = 24 Divide each side by '1'. z = 24 Simplifying z = 24
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