Identify the solution set of |x + 3| + 7 less than or equal to 10 and describe the graph in a complete sentence.

Question

anonymous · Answer

This is it?

$|x + 3| + 7 \le 10$

anonymous · Answer

Okay, first we subtract 7 to both sides, what's 10 - 7?

anonymous · Answer

3.

anonymous · Answer

what do u think I agree with @iGreen.

anonymous · Answer

Yes, so we have:

$|x + 3| \le 3$

Now we break this into two inequalities.

$x + 3 \le 3$

and

$-x - 3 \le 3$

(Note: We multiplied -1 to every term inside the absolute value brackets)

Let's solve each of these separately.

$x + 3 \le 3$

Subtract 3 to both sides, what's 3 - 3?

anonymous · Answer

0.

anonymous · Answer

Yes, so we have:

$x \le 0$

$-x - 3 \le 3$

Add 3 to both sides, what's 3 + 3?

anonymous · Answer

6

anonymous · Answer

Yes, so we have:

$-x \le 6$

Now we divide -1 to both sides, what's 6 / -1?

anonymous · Answer

-6

anonymous · Answer

Yes, so we have:

$x \ge -6$

(Remember, we switch the sign when multiplying or dividing by a negative number)

So we have:

$x \le 0$

and

$x \ge -6$

This will look like:|dw:1424093796374:dw|