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Simplifying -4(z + 3) + -3(4 + -1z) = 5(z + -2) + -2 Reorder the terms: -4(3 + z) + -3(4 + -1z) = 5(z + -2) + -2 (3 * -4 + z * -4) + -3(4 + -1z) = 5(z + -2) + -2 (-12 + -4z) + -3(4 + -1z) = 5(z + -2) + -2 -12 + -4z + (4 * -3 + -1z * -3) = 5(z + -2) + -2 -12 + -4z + (-12 + 3z) = 5(z + -2) + -2 Reorder the terms: -12 + -12 + -4z + 3z = 5(z + -2) + -2 Combine like terms: -12 + -12 = -24 -24 + -4z + 3z = 5(z + -2) + -2 Combine like terms: -4z + 3z = -1z -24 + -1z = 5(z + -2) + -2 Reorder the terms: -24 + -1z = 5(-2 + z) + -2 -24 + -1z = (-2 * 5 + z * 5) + -2 -24 + -1z = (-10 + 5z) + -2 Reorder the terms: -24 + -1z = -10 + -2 + 5z Combine like terms: -10 + -2 = -12 -24 + -1z = -12 + 5z Solving -24 + -1z = -12 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -24 + -1z + -5z = -12 + 5z + -5z Combine like terms: -1z + -5z = -6z -24 + -6z = -12 + 5z + -5z Combine like terms: 5z + -5z = 0 -24 + -6z = -12 + 0 -24 + -6z = -12 Add '24' to each side of the equation. -24 + 24 + -6z = -12 + 24 Combine like terms: -24 + 24 = 0 0 + -6z = -12 + 24 -6z = -12 + 24 Combine like terms: -12 + 24 = 12 -6z = 12 Divide each side by '-6'. z = -2 Simplifying z = -2
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