1. ## Inequalities?

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

2. Originally Posted by federer
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
$|2x - 1| = 2x - 1\,$ for $2x -1 \geq 0 \Rightarrow x \geq \frac{1}{2}$.
$|2x - 1| = -(2x - 1)\,$ for $2x -1 < 0 \Rightarrow x < \frac{1}{2}$.

(a) Solve 2x - 1 < 5 => x < 3 AND $x \geq \frac{1}{2}$: $\frac{1}{2} \leq x < 3$.

Solve -(2x - 1) < 5 => x > -2 AND $x < \frac{1}{2}$: $-2 < x < \frac{1}{2}$.

So the answer is $\frac{1}{2} \leq x < 3$ combined with $-2 < x < \frac{1}{2}$. You can "express [this] solution in both set notation and interval notation".

Do (b) in a similar way.