Recall that

$|$x $+10|=$

x $+10$x $10($x $+10)$x $<10.$

Therefore, we will need to check the limits when approaching from the left and from the right.

We will start by checking the limit when approaching from the left. As x approaches

$10$

from the left, we have

lim$$x$10$

$7$x $+70|$x $+10|$

$=$lim$$x$10$

$7$x $+70$

$7$