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Simplifying -5(z + 3) + 3(3z + -3) = 3(z + -5) + 8 Reorder the terms: -5(3 + z) + 3(3z + -3) = 3(z + -5) + 8 (3 * -5 + z * -5) + 3(3z + -3) = 3(z + -5) + 8 (-15 + -5z) + 3(3z + -3) = 3(z + -5) + 8 Reorder the terms: -15 + -5z + 3(-3 + 3z) = 3(z + -5) + 8 -15 + -5z + (-3 * 3 + 3z * 3) = 3(z + -5) + 8 -15 + -5z + (-9 + 9z) = 3(z + -5) + 8 Reorder the terms: -15 + -9 + -5z + 9z = 3(z + -5) + 8 Combine like terms: -15 + -9 = -24 -24 + -5z + 9z = 3(z + -5) + 8 Combine like terms: -5z + 9z = 4z -24 + 4z = 3(z + -5) + 8 Reorder the terms: -24 + 4z = 3(-5 + z) + 8 -24 + 4z = (-5 * 3 + z * 3) + 8 -24 + 4z = (-15 + 3z) + 8 Reorder the terms: -24 + 4z = -15 + 8 + 3z Combine like terms: -15 + 8 = -7 -24 + 4z = -7 + 3z Solving -24 + 4z = -7 + 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. -24 + 4z + -3z = -7 + 3z + -3z Combine like terms: 4z + -3z = 1z -24 + 1z = -7 + 3z + -3z Combine like terms: 3z + -3z = 0 -24 + 1z = -7 + 0 -24 + 1z = -7 Add '24' to each side of the equation. -24 + 24 + 1z = -7 + 24 Combine like terms: -24 + 24 = 0 0 + 1z = -7 + 24 1z = -7 + 24 Combine like terms: -7 + 24 = 17 1z = 17 Divide each side by '1'. z = 17 Simplifying z = 17
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