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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