# How do you solve abs(4x-3)<7?

Jul 28, 2016

$- 1 < x < 2.5$ - i.e. $x$ is between $- 1$ and $2.5$

#### Explanation:

As $| 4 x - 3 | < 7$,

either $4 x - 3 < 7$ i.e, $4 x < 7 + 3$ or

$4 x = 10$ i.e. $x < \frac{10}{4}$ i.e. $x < 2.5$

or $- \left(4 x - 3\right) < 7$ i.e. $- 4 x + 3 < 7$ or

$3 - 7 < 4 x$ or $4 x \succ 4$ i.e. $x \succ 1$

Hence, we have $x < 2.5$ and $x \succ 1$, which can be written better as

$- 1 < x < 2.5$ - i.e. $x$ is between $- 1$ and $2.5$