Solve absolute value inequality. |3-(3/4x)|>9

zgribestika

zgribestika

Answered question

2021-12-08

Solve absolute value inequality.
|3-(3/4x)|>9

Answer & Explanation

Alex Sheppard

Alex Sheppard

Beginner2021-12-09Added 36 answers

Step 1
Solution -
Given inequality -
|334x|>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-
334x>9 and,
334x<9
When,
334x>9
12x-3>36x
24x<-3
x<324
x<18
When,
334x<9
3x-3<-36x
39x<3
x<113
Hence from above two intervals of x we get absolute value for inequality as in -
x<18

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