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Section 2.2 : Linear Equations

Solve each of the following equations and check your answer.

1. \(13 + 2\left( {1 - u} \right) = 8u - 5\left( {u + 7} \right)\)
2. \(8\left( {2 + 3z} \right) + 1 = z - 10\left( {z + 1} \right)\)
3. \(8 - \left( {4 - 12t} \right) + 2 = 3t + 2\left( {7 - 3t} \right)\)
4. \(2x\left( {6x - 1} \right) + 21 = 8x - x\left( {3 - 12x} \right)\)
5. \(\displaystyle \frac{{3w - 1}}{5} + 1 = \frac{{7w + 2}}{{15}}\)
6. \(\displaystyle \frac{{10y}}{9} + \frac{1}{3} = \frac{{2y - 1}}{9}\)
7. \(2\left( {3 - \frac{x}{4}} \right) = \frac{{2x + 5}}{3} - \frac{1}{3}\)
8. \(\displaystyle \frac{{6x + 24}}{{x + 4}} = 5\)
9. \(\displaystyle \frac{3}{{v + 7}} - \frac{{2 - 7v}}{{{v^2} + 5v - 14}} = \frac{4}{{v - 2}}\)
10. \(\displaystyle \frac{{6t - 1}}{{{t^2} + 5t + 4}} = - \frac{{19}}{{t + 1}}\)
11. \(\displaystyle \frac{{8 - 4z}}{{3z - 2}} = 2 - \frac{{10z}}{{3z - 2}}\)
12. \(\displaystyle \frac{{4w - 1}}{{w - 2}} + \frac{{8w}}{{{w^2} - 6w + 8}} = \frac{{4w + 3}}{{w - 4}}\)