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Simplifying -5(z + 1) + 3(3z + -5) = 3(z + -4) + 14 Reorder the terms: -5(1 + z) + 3(3z + -5) = 3(z + -4) + 14 (1 * -5 + z * -5) + 3(3z + -5) = 3(z + -4) + 14 (-5 + -5z) + 3(3z + -5) = 3(z + -4) + 14 Reorder the terms: -5 + -5z + 3(-5 + 3z) = 3(z + -4) + 14 -5 + -5z + (-5 * 3 + 3z * 3) = 3(z + -4) + 14 -5 + -5z + (-15 + 9z) = 3(z + -4) + 14 Reorder the terms: -5 + -15 + -5z + 9z = 3(z + -4) + 14 Combine like terms: -5 + -15 = -20 -20 + -5z + 9z = 3(z + -4) + 14 Combine like terms: -5z + 9z = 4z -20 + 4z = 3(z + -4) + 14 Reorder the terms: -20 + 4z = 3(-4 + z) + 14 -20 + 4z = (-4 * 3 + z * 3) + 14 -20 + 4z = (-12 + 3z) + 14 Reorder the terms: -20 + 4z = -12 + 14 + 3z Combine like terms: -12 + 14 = 2 -20 + 4z = 2 + 3z Solving -20 + 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. -20 + 4z + -3z = 2 + 3z + -3z Combine like terms: 4z + -3z = 1z -20 + 1z = 2 + 3z + -3z Combine like terms: 3z + -3z = 0 -20 + 1z = 2 + 0 -20 + 1z = 2 Add '20' to each side of the equation. -20 + 20 + 1z = 2 + 20 Combine like terms: -20 + 20 = 0 0 + 1z = 2 + 20 1z = 2 + 20 Combine like terms: 2 + 20 = 22 1z = 22 Divide each side by '1'. z = 22 Simplifying z = 22
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