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### Section 2-11 : Linear Inequalities

For problems 1 – 6 solve each of the following inequalities. Give the solution in both inequality and interval notations.

1. $$4\left( {z + 2} \right) - 1 > 5 - 7\left( {4 - z} \right)$$ Solution
2. $$\displaystyle \frac{1}{2}\left( {3 + 4t} \right) \le 6\left( {\frac{1}{3} - \frac{1}{2}t} \right) - \frac{1}{4}\left( {2 + 10t} \right)$$ Solution
3. $$- 1 < 4x + 2 < 10$$ Solution
4. $$8 \le 3 - 5z < 12$$ Solution
5. $$0 \le 10w - 15 \le 23$$ Solution
6. $$\displaystyle 2 < \frac{1}{6} - \frac{1}{2}x \le 4$$ Solution
7. If $$0 \le x < 3$$ determine a and b for the inequality : $$a \le 4x + 1 < b$$ Solution