Jamarcus Spears

2023-03-11

How to graph and solve $|4x–3|+2<11$?

Anastasia Lee

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

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