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Simplifying 11(2 + 4) + -2(z + -4) = 4(z + 3) + 4(z + -2) Combine like terms: 2 + 4 = 6 11(6) + -2(z + -4) = 4(z + 3) + 4(z + -2) Multiply 11 * 6 66 + -2(z + -4) = 4(z + 3) + 4(z + -2) Reorder the terms: 66 + -2(-4 + z) = 4(z + 3) + 4(z + -2) 66 + (-4 * -2 + z * -2) = 4(z + 3) + 4(z + -2) 66 + (8 + -2z) = 4(z + 3) + 4(z + -2) Combine like terms: 66 + 8 = 74 74 + -2z = 4(z + 3) + 4(z + -2) Reorder the terms: 74 + -2z = 4(3 + z) + 4(z + -2) 74 + -2z = (3 * 4 + z * 4) + 4(z + -2) 74 + -2z = (12 + 4z) + 4(z + -2) Reorder the terms: 74 + -2z = 12 + 4z + 4(-2 + z) 74 + -2z = 12 + 4z + (-2 * 4 + z * 4) 74 + -2z = 12 + 4z + (-8 + 4z) Reorder the terms: 74 + -2z = 12 + -8 + 4z + 4z Combine like terms: 12 + -8 = 4 74 + -2z = 4 + 4z + 4z Combine like terms: 4z + 4z = 8z 74 + -2z = 4 + 8z Solving 74 + -2z = 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. 74 + -2z + -8z = 4 + 8z + -8z Combine like terms: -2z + -8z = -10z 74 + -10z = 4 + 8z + -8z Combine like terms: 8z + -8z = 0 74 + -10z = 4 + 0 74 + -10z = 4 Add '-74' to each side of the equation. 74 + -74 + -10z = 4 + -74 Combine like terms: 74 + -74 = 0 0 + -10z = 4 + -74 -10z = 4 + -74 Combine like terms: 4 + -74 = -70 -10z = -70 Divide each side by '-10'. z = 7 Simplifying z = 7
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