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Simplifying 38(z + 2) = 34(z + 3) Reorder the terms: 38(2 + z) = 34(z + 3) (2 * 38 + z * 38) = 34(z + 3) (76 + 38z) = 34(z + 3) Reorder the terms: 76 + 38z = 34(3 + z) 76 + 38z = (3 * 34 + z * 34) 76 + 38z = (102 + 34z) Solving 76 + 38z = 102 + 34z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-34z' to each side of the equation. 76 + 38z + -34z = 102 + 34z + -34z Combine like terms: 38z + -34z = 4z 76 + 4z = 102 + 34z + -34z Combine like terms: 34z + -34z = 0 76 + 4z = 102 + 0 76 + 4z = 102 Add '-76' to each side of the equation. 76 + -76 + 4z = 102 + -76 Combine like terms: 76 + -76 = 0 0 + 4z = 102 + -76 4z = 102 + -76 Combine like terms: 102 + -76 = 26 4z = 26 Divide each side by '4'. z = 6.5 Simplifying z = 6.5
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