Question

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

Answer 1

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