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

Question

1690 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-28T17:37:36

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

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

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

$4x=10$ i.e. $x<10/4$ i.e. $x<2.5$

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

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

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

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

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