Question

What is the solution set, in interval notation, to the following inequality? -2||x+1|+4>-6

Answer 1

Recall that:

`\begin{gathered} |a|-b\text{.} \end{gathered}`

Subtracting 4 from the given equation we get:

`\begin{gathered} -2|x+1|+4-4>-6-4, \\ -2|x+1|>-10. \end{gathered}`

Now, the above inequality is equivalent to the following one:

`2|x+1|<10.`

Now, multiplying the above inequality by 1/2 we get:

`\begin{gathered} 2|x+1|\cdot(1)/(2)<10\cdot(1)/(2), \\ |x+1|<5. \end{gathered}`

Now, the above inequality is equivalent to the following one:

Answer:

`(-6,4)\text{.}`