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Simplifying 7z + 2(z + -12) = 2(z + -13) + 3(2z + 1) Reorder the terms: 7z + 2(-12 + z) = 2(z + -13) + 3(2z + 1) 7z + (-12 * 2 + z * 2) = 2(z + -13) + 3(2z + 1) 7z + (-24 + 2z) = 2(z + -13) + 3(2z + 1) Reorder the terms: -24 + 7z + 2z = 2(z + -13) + 3(2z + 1) Combine like terms: 7z + 2z = 9z -24 + 9z = 2(z + -13) + 3(2z + 1) Reorder the terms: -24 + 9z = 2(-13 + z) + 3(2z + 1) -24 + 9z = (-13 * 2 + z * 2) + 3(2z + 1) -24 + 9z = (-26 + 2z) + 3(2z + 1) Reorder the terms: -24 + 9z = -26 + 2z + 3(1 + 2z) -24 + 9z = -26 + 2z + (1 * 3 + 2z * 3) -24 + 9z = -26 + 2z + (3 + 6z) Reorder the terms: -24 + 9z = -26 + 3 + 2z + 6z Combine like terms: -26 + 3 = -23 -24 + 9z = -23 + 2z + 6z Combine like terms: 2z + 6z = 8z -24 + 9z = -23 + 8z Solving -24 + 9z = -23 + 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. -24 + 9z + -8z = -23 + 8z + -8z Combine like terms: 9z + -8z = 1z -24 + 1z = -23 + 8z + -8z Combine like terms: 8z + -8z = 0 -24 + 1z = -23 + 0 -24 + 1z = -23 Add '24' to each side of the equation. -24 + 24 + 1z = -23 + 24 Combine like terms: -24 + 24 = 0 0 + 1z = -23 + 24 1z = -23 + 24 Combine like terms: -23 + 24 = 1 1z = 1 Divide each side by '1'. z = 1 Simplifying z = 1
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