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Simplifying -42 + -2(3z + -5) = 4z + -4(1 + -1z) Reorder the terms: -42 + -2(-5 + 3z) = 4z + -4(1 + -1z) -42 + (-5 * -2 + 3z * -2) = 4z + -4(1 + -1z) -42 + (10 + -6z) = 4z + -4(1 + -1z) Combine like terms: -42 + 10 = -32 -32 + -6z = 4z + -4(1 + -1z) -32 + -6z = 4z + (1 * -4 + -1z * -4) -32 + -6z = 4z + (-4 + 4z) Reorder the terms: -32 + -6z = -4 + 4z + 4z Combine like terms: 4z + 4z = 8z -32 + -6z = -4 + 8z Solving -32 + -6z = -4 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -32 + -6z + -8z = -4 + 8z + -8z Combine like terms: -6z + -8z = -14z -32 + -14z = -4 + 8z + -8z Combine like terms: 8z + -8z = 0 -32 + -14z = -4 + 0 -32 + -14z = -4 Add '32' to each side of the equation. -32 + 32 + -14z = -4 + 32 Combine like terms: -32 + 32 = 0 0 + -14z = -4 + 32 -14z = -4 + 32 Combine like terms: -4 + 32 = 28 -14z = 28 Divide each side by '-14'. z = -2 Simplifying z = -2
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