Algebra

Let's split the inequality into two different inequalities and find the overlapping numbers. 

Now, let's find an interval for x from both inequalities and find the overlapping zone.

Alright. So we have the two inequalities 

$1-3x < x+8\space\space\space\space\space(1)\\ x + 8 \le 7-x\space\space\space\space\space\space(2)$

From the first inequality, we have

$1-3x -7/4$

From the second inequality, we have

$x+8 \leq 7-x\\ 2x \leq -1\\ x \leq -1/2$

Thus, we have the intervals

$x>-\frac{7}{4}\quad \mathrm{and}\quad \:x\le \:-\frac{1}{2}$

In interval notation, this is $(-\frac{7}{4},\:-\frac{1}{2}]$

Thanks! :)

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