# How do you solve and write the following in interval notation:  2 < 2x + 4 < 10?

Jul 14, 2017

$\left(- 1 , 3\right)$

#### Explanation:

As $2 < 2 x + 4 < 10$

we have $2 < 2 x + 4$ or $2 - 4 < 2 x$ i.e. $- 1 < x$

Further, as $2 x + 4 < 10$, we have $2 x < 6$ or $x < 3$

Hence we have $- 1 < x < 3$,

which in interval notation can be written as $\left(- 1 , 3\right)$

Note: Had it been $- 1 \le x < 3$, we would have written $\left[- 1 , 3\right)$ i.e. for inequality with equality we use square brackets and for pure inequality we use small brackets.