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Simplifying 8(2 + 3) + -3(2 + -4) = 2(2 + -4) + 2(z + -3) Combine like terms: 2 + 3 = 5 8(5) + -3(2 + -4) = 2(2 + -4) + 2(z + -3) Multiply 8 * 5 40 + -3(2 + -4) = 2(2 + -4) + 2(z + -3) Combine like terms: 2 + -4 = -2 40 + -3(-2) = 2(2 + -4) + 2(z + -3) Multiply -3 * -2 40 + 6 = 2(2 + -4) + 2(z + -3) Combine like terms: 40 + 6 = 46 46 = 2(2 + -4) + 2(z + -3) Combine like terms: 2 + -4 = -2 46 = 2(-2) + 2(z + -3) Multiply 2 * -2 46 = -4 + 2(z + -3) Reorder the terms: 46 = -4 + 2(-3 + z) 46 = -4 + (-3 * 2 + z * 2) 46 = -4 + (-6 + 2z) Combine like terms: -4 + -6 = -10 46 = -10 + 2z Solving 46 = -10 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 46 + -2z = -10 + 2z + -2z Combine like terms: 2z + -2z = 0 46 + -2z = -10 + 0 46 + -2z = -10 Add '-46' to each side of the equation. 46 + -46 + -2z = -10 + -46 Combine like terms: 46 + -46 = 0 0 + -2z = -10 + -46 -2z = -10 + -46 Combine like terms: -10 + -46 = -56 -2z = -56 Divide each side by '-2'. z = 28 Simplifying z = 28
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