zgribestika

2021-12-08

Solve absolute value inequality.

|3-(3/4x)|>9

|3-(3/4x)|>9

Alex Sheppard

Beginner2021-12-09Added 36 answers

Step 1

Solution -

Given inequality -

$|3-\frac{3}{4x}|>9$

While removing the mod from the left side it reflects positive and negative sign to the function on other side of inequality.

In case of + sign, there is no change in the inequality sign.

But in case of - sign the inequality sign reverses. For e.g, less < becomes greater than > and vice versa.

Step 2

Now solving the inequality we get-

$3-\frac{3}{4x}>9$ and,

$3-\frac{3}{4x}<-9$

When,

$3-\frac{3}{4x}>9$

12x-3>36x

24x<-3

$x<-\frac{3}{24}$

$x<-\frac{1}{8}$

When,

$3-\frac{3}{4x}<-9$

3x-3<-36x

39x<3

$x<\frac{1}{13}$

Hence from above two intervals of x we get absolute value for inequality as in -

$x<-\frac{1}{8}$

Solution -

Given inequality -

While removing the mod from the left side it reflects positive and negative sign to the function on other side of inequality.

In case of + sign, there is no change in the inequality sign.

But in case of - sign the inequality sign reverses. For e.g, less < becomes greater than > and vice versa.

Step 2

Now solving the inequality we get-

When,

12x-3>36x

24x<-3

When,

3x-3<-36x

39x<3

Hence from above two intervals of x we get absolute value for inequality as in -

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