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Simplifying 3(4z + -1) + -2(z + 3) = 7(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 3) = 7(z + 1) (-1 * 3 + 4z * 3) + -2(z + 3) = 7(z + 1) (-3 + 12z) + -2(z + 3) = 7(z + 1) Reorder the terms: -3 + 12z + -2(3 + z) = 7(z + 1) -3 + 12z + (3 * -2 + z * -2) = 7(z + 1) -3 + 12z + (-6 + -2z) = 7(z + 1) Reorder the terms: -3 + -6 + 12z + -2z = 7(z + 1) Combine like terms: -3 + -6 = -9 -9 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -9 + 10z = 7(z + 1) Reorder the terms: -9 + 10z = 7(1 + z) -9 + 10z = (1 * 7 + z * 7) -9 + 10z = (7 + 7z) Solving -9 + 10z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -9 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -9 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -9 + 3z = 7 + 0 -9 + 3z = 7 Add '9' to each side of the equation. -9 + 9 + 3z = 7 + 9 Combine like terms: -9 + 9 = 0 0 + 3z = 7 + 9 3z = 7 + 9 Combine like terms: 7 + 9 = 16 3z = 16 Divide each side by '3'. z = 5.333333333 Simplifying z = 5.333333333
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