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Simplifying -16(z + 1) + 5(4z + -5) = 3(z + -4) + 13 Reorder the terms: -16(1 + z) + 5(4z + -5) = 3(z + -4) + 13 (1 * -16 + z * -16) + 5(4z + -5) = 3(z + -4) + 13 (-16 + -16z) + 5(4z + -5) = 3(z + -4) + 13 Reorder the terms: -16 + -16z + 5(-5 + 4z) = 3(z + -4) + 13 -16 + -16z + (-5 * 5 + 4z * 5) = 3(z + -4) + 13 -16 + -16z + (-25 + 20z) = 3(z + -4) + 13 Reorder the terms: -16 + -25 + -16z + 20z = 3(z + -4) + 13 Combine like terms: -16 + -25 = -41 -41 + -16z + 20z = 3(z + -4) + 13 Combine like terms: -16z + 20z = 4z -41 + 4z = 3(z + -4) + 13 Reorder the terms: -41 + 4z = 3(-4 + z) + 13 -41 + 4z = (-4 * 3 + z * 3) + 13 -41 + 4z = (-12 + 3z) + 13 Reorder the terms: -41 + 4z = -12 + 13 + 3z Combine like terms: -12 + 13 = 1 -41 + 4z = 1 + 3z Solving -41 + 4z = 1 + 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. -41 + 4z + -3z = 1 + 3z + -3z Combine like terms: 4z + -3z = 1z -41 + 1z = 1 + 3z + -3z Combine like terms: 3z + -3z = 0 -41 + 1z = 1 + 0 -41 + 1z = 1 Add '41' to each side of the equation. -41 + 41 + 1z = 1 + 41 Combine like terms: -41 + 41 = 0 0 + 1z = 1 + 41 1z = 1 + 41 Combine like terms: 1 + 41 = 42 1z = 42 Divide each side by '1'. z = 42 Simplifying z = 42
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