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Simplifying 4(6z + -1) + -3(z + 6) = 7(z + 1) Reorder the terms: 4(-1 + 6z) + -3(z + 6) = 7(z + 1) (-1 * 4 + 6z * 4) + -3(z + 6) = 7(z + 1) (-4 + 24z) + -3(z + 6) = 7(z + 1) Reorder the terms: -4 + 24z + -3(6 + z) = 7(z + 1) -4 + 24z + (6 * -3 + z * -3) = 7(z + 1) -4 + 24z + (-18 + -3z) = 7(z + 1) Reorder the terms: -4 + -18 + 24z + -3z = 7(z + 1) Combine like terms: -4 + -18 = -22 -22 + 24z + -3z = 7(z + 1) Combine like terms: 24z + -3z = 21z -22 + 21z = 7(z + 1) Reorder the terms: -22 + 21z = 7(1 + z) -22 + 21z = (1 * 7 + z * 7) -22 + 21z = (7 + 7z) Solving -22 + 21z = 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. -22 + 21z + -7z = 7 + 7z + -7z Combine like terms: 21z + -7z = 14z -22 + 14z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -22 + 14z = 7 + 0 -22 + 14z = 7 Add '22' to each side of the equation. -22 + 22 + 14z = 7 + 22 Combine like terms: -22 + 22 = 0 0 + 14z = 7 + 22 14z = 7 + 22 Combine like terms: 7 + 22 = 29 14z = 29 Divide each side by '14'. z = 2.071428571 Simplifying z = 2.071428571
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