Answer:
The solution to the given inequality is:
[tex]1<x<7[/tex] i.e. in the interval form it is given by: (1,7)
Step-by-step explanation:
We are given a inequality in term of variable x as follows:
[tex]|x-4|<3[/tex]
Now, we know that any inequality with modulus function is opened as follows:
If
[tex]|x-a|<b[/tex]
Then we have:
[tex]-b<x-a<b[/tex]
i.e. we may write it as:
[tex]a-b<x<a+b[/tex]
Here in the given expression we have:
a=4 and b=3
Hence, the solution is given by:
[tex]4-3<x<4+3\\\\i.e.\\\\1<x<7[/tex]
