Solve the following inequality. Put your answers in interval notation . |2×+1|<5

Question

asked Mar 4, 2023 37.3k views

1 Answer

Benoit Jadinon · Answer 1 · 2023-03-10T11:03:03+0000

To solve that inequality we must divide it into two parts, remember that

$|x|=\begin{cases}x,x>0 \\ -x,x<0\end{cases}$

Then we can write

$\begin{gathered} |2x+1|<5\Rightarrow\begin{cases}2x+1<5 \\ -(2x+1)<5\end{cases} \\ \end{gathered}$

Now we have two inequalities:

$\begin{gathered} 2x+1<5 \\ -2x-1<5 \end{gathered}$

Let's solve the first one:

$\begin{gathered} 2x+1<5 \\ \\ 2x<5-1 \\ \\ 2x<4 \\ \\ x<(4)/(2) \\ \\ x<2 \end{gathered}$

And the second one

$\begin{gathered} -2x-1<5 \\ \\ -2x<5+1 \\ \\ -2x<6 \\ \\ -x<(6)/(2) \\ \\ -x<3 \\ \\ x>-3 \end{gathered}$

Then we have two solutions:

$x<2\text{ and }x>-3$

Writing it in interval notation

[tex]-3