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Simplifying 3(4z + -1) + -2(z + 8) = 7(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 8) = 7(z + 1) (-1 * 3 + 4z * 3) + -2(z + 8) = 7(z + 1) (-3 + 12z) + -2(z + 8) = 7(z + 1) Reorder the terms: -3 + 12z + -2(8 + z) = 7(z + 1) -3 + 12z + (8 * -2 + z * -2) = 7(z + 1) -3 + 12z + (-16 + -2z) = 7(z + 1) Reorder the terms: -3 + -16 + 12z + -2z = 7(z + 1) Combine like terms: -3 + -16 = -19 -19 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -19 + 10z = 7(z + 1) Reorder the terms: -19 + 10z = 7(1 + z) -19 + 10z = (1 * 7 + z * 7) -19 + 10z = (7 + 7z) Solving -19 + 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. -19 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -19 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -19 + 3z = 7 + 0 -19 + 3z = 7 Add '19' to each side of the equation. -19 + 19 + 3z = 7 + 19 Combine like terms: -19 + 19 = 0 0 + 3z = 7 + 19 3z = 7 + 19 Combine like terms: 7 + 19 = 26 3z = 26 Divide each side by '3'. z = 8.666666667 Simplifying z = 8.666666667
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