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:

$2|x+1|$

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

$\begin{gathered} 2|x+1|\cdot\frac{1}{2}$

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

$-5Subtracting 1 from the above result we get:[tex]\begin{gathered} -5-1Finally, the above inequality in interval notation is:[tex](-6,4)\text{.}$

Answer:

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