Solve the following inequalities and express your solution in both set notation and interval notation:
(a) | 2x - 1 | < 5
(b) | 2x - 1 | > 5
Need workings. Answer should be in set & interval notation
$\displaystyle |2x - 1| = 2x - 1\,$ for $\displaystyle 2x -1 \geq 0 \Rightarrow x \geq \frac{1}{2}$.
$\displaystyle |2x - 1| = -(2x - 1)\,$ for $\displaystyle 2x -1 < 0 \Rightarrow x < \frac{1}{2}$.
(a) Solve 2x - 1 < 5 => x < 3 AND $\displaystyle x \geq \frac{1}{2}$: $\displaystyle \frac{1}{2} \leq x < 3$.
Solve -(2x - 1) < 5 => x > -2 AND $\displaystyle x < \frac{1}{2}$: $\displaystyle -2 < x < \frac{1}{2}$.
So the answer is $\displaystyle \frac{1}{2} \leq x < 3$ combined with $\displaystyle -2 < x < \frac{1}{2}$. You can "express [this] solution in both set notation and interval notation".
Do (b) in a similar way.