How to graph and solve |4x-3|+2<11?

Jamarcus Spears

Jamarcus Spears

Answered question

2023-03-11

How to graph and solve | 4 x 3 | + 2 < 11 ?

Answer & Explanation

Anastasia Lee

Anastasia Lee

Beginner2023-03-12Added 5 answers

The inequality is
| 4 x - 3 | + 2 < 11
| 4 x - 3 | - 9 < 0
The point to consider is
4 x - 3 = 0
x = 3 4
There are 2 intervals to consider
( - , 3 4 ) and ( 3 4 , + )
Hence,
In the first interval
- 4 x + 3 - 9 < 0
- 4 x - 6 < 0
4 x > - 6
x > - 3 2
This is located in the interval.
In the second interval
4 x - 3 - 9 < 0
4 x - 12 < 0
x < 3
This is located in the interval.
The answer is x ( - 3 2 , 3 )
graph{|4x-3|-9 [-20.27, 20.27, -10.14, 10.14]}

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