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Simplifying -16(z + 1) + 5(4z + -6) = 3(z + -4) + 9 Reorder the terms: -16(1 + z) + 5(4z + -6) = 3(z + -4) + 9 (1 * -16 + z * -16) + 5(4z + -6) = 3(z + -4) + 9 (-16 + -16z) + 5(4z + -6) = 3(z + -4) + 9 Reorder the terms: -16 + -16z + 5(-6 + 4z) = 3(z + -4) + 9 -16 + -16z + (-6 * 5 + 4z * 5) = 3(z + -4) + 9 -16 + -16z + (-30 + 20z) = 3(z + -4) + 9 Reorder the terms: -16 + -30 + -16z + 20z = 3(z + -4) + 9 Combine like terms: -16 + -30 = -46 -46 + -16z + 20z = 3(z + -4) + 9 Combine like terms: -16z + 20z = 4z -46 + 4z = 3(z + -4) + 9 Reorder the terms: -46 + 4z = 3(-4 + z) + 9 -46 + 4z = (-4 * 3 + z * 3) + 9 -46 + 4z = (-12 + 3z) + 9 Reorder the terms: -46 + 4z = -12 + 9 + 3z Combine like terms: -12 + 9 = -3 -46 + 4z = -3 + 3z Solving -46 + 4z = -3 + 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. -46 + 4z + -3z = -3 + 3z + -3z Combine like terms: 4z + -3z = 1z -46 + 1z = -3 + 3z + -3z Combine like terms: 3z + -3z = 0 -46 + 1z = -3 + 0 -46 + 1z = -3 Add '46' to each side of the equation. -46 + 46 + 1z = -3 + 46 Combine like terms: -46 + 46 = 0 0 + 1z = -3 + 46 1z = -3 + 46 Combine like terms: -3 + 46 = 43 1z = 43 Divide each side by '1'. z = 43 Simplifying z = 43
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