Recall that:
[tex]\begin{gathered} |a|-b\text{.} \end{gathered}[/tex]
Subtracting 4 from the given equation we get:
[tex]\begin{gathered} -2|x+1|+4-4>-6-4, \\ -2|x+1|>-10. \end{gathered}[/tex]
Now, the above inequality is equivalent to the following one:
[tex]2|x+1|<10.[/tex]
Now, multiplying the above inequality by 1/2 we get:
[tex]\begin{gathered} 2|x+1|\cdot\frac{1}{2}<10\cdot\frac{1}{2}, \\ |x+1|<5. \end{gathered}[/tex]
Now, the above inequality is equivalent to the following one:
[tex]-5Subtracting 1 from the above result we get:[tex]\begin{gathered} -5-1Finally, the above inequality in interval notation is:[tex](-6,4)\text{.}[/tex]
Answer:
[tex](-6,4)\text{.}[/tex]
