Question

|3x-4|>10 solve inequality

Answer 1

In solving absolute inequality,

it is important to find when the absolute value changes.

• When $\sf{3x-4\geq 0}$ [ $\sf{x\geq \dfrac{4}{3} }$ ]

• We have to solve $\sf{+(3x-4)>10}$

We get $\sf{x>\dfrac{14}{3} }$

And it is a solution for the given case.

• When $\sf{3x-4<0}$ [ $\sf{x< \dfrac{4}{3} }$ ]

• We have to solve $\sf{-(3x-4)>10}$

We get $\sf{x<-2}$

And it is a solution for the given case.

Answer

∴$\sf{x<-2}$ or $\sf{x>\dfrac{14}{3} }$

Additional Information

1. The absolute value is always not negative.

Therefore we cannot solve such as

• $\sf{|x|<-10}$

2. To remove the absolute value,

it is important to know when the inside becomes positive, 0, or negative.