# How do you solve and write the following in interval notation: #x + 2 > -3# and #x + 2 <5#?

##### 1 Answer

#### Explanation:

Each one of these two inequalities has a set of

From the first inequality, we have

#x+2> "-"3 => x+2- color(blue)(2)>"-3" - color(blue)(2)#

#color(white)(x+2> "-"3) => x" ">"-5"#

Alright; so the first inequality is true for every

Similarly, we can solve the second inequality as follows:

#x+2<5 => x+2-color(blue)2 < 5 - color(blue)2#

#color(white)(x+2<5) => x" "<3#

Okay, so the second inequality is true for every

We then ask ourselves: where do these two sets overlap? In other words, what values of *both* inequalities true? We can graph both sets on a number line to help us see this:

<————— -5 ————— 0 ——— 3 —————>

From the number line above, we see that the two solutions overlap between

which, as we can see from the number line, simplifies to