Answer:
[tex]\displaystyle x\in \left(-\frac{40}{13},\frac{48}{13}\right)[/tex]
Step-by-step explanation:
Inequalities with Absolute Value
We must recall the following rule:
[tex]\text{If }|M|<N,\ N>0[/tex]
Then:
[tex]-N<M<N[/tex]
We have the following inequality:
[tex]|13x-4|+12 < 56[/tex]
Subtracting 12:
[tex]|13x-4|< 56-12[/tex]
[tex]|13x-4|< 44[/tex]
Applying the rule:
[tex]-44<13x-4<44[/tex]
Adding 4:
[tex]-44+4<13x<44+4[/tex]
Operating:
[tex]-40<13x<48[/tex]
Dividing by 13:
[tex]\displaystyle -\frac{40}{13}<x<\frac{48}{13}[/tex]
The solution expressed in interval form is:
[tex]\boxed{\displaystyle x\in \left(-\frac{40}{13},\frac{48}{13}\right)}[/tex]
