-1<3-5m<3

## How do you solve and graph an inequality if there are 2 inequality signs?

# 4 Answers

Hey No.... the "m" is between two "fences" ,,, when m=0, the <3 fence is touched ... when m=1, the >-1 fence is crossed -- step back to m= 0.8 ... Best wishes :)

- 1 < 3 - 5m < 3

↑ ↑ ↑

* less greater greatest*

-1 < 3 - 5m < 3

-3 -3 -3

- 4 < - 5m < 0

÷ (-5) ÷ (-5) ÷ (-5)

0.8 > m > 0

↑ ↑ ↑

*greatest greater less *

Let's rewrite inequality from less to greatest

* 0 < m < 0.8 or* all real numbers out of interval

**(0, 0.8)**<———o——————o————>

0 0.8

You use the same principles as if there's only one inequality sign.

But if it makes it easier for you, divide the problem into two separate inequalities:

-1 < 3 - 5m < 3 is the same thing as saying that -1 < 3 - 5m and 3 - 5m < 3.

Now, normal inequality rules apply. First subtract both sides by 3 for both equations:

-4 < -5m and -5m < 0

Then, divide by -5. Remember to reverse the sign direction because you're dividing by a negative:

m < 4/5 and m > 0.

So 0 < m < 4/5. You can verify the answer by throwing a number in between the two values.

And there you have it: inequalities with 2 signs are just two single-sign inequalities put together.

Solve first,

Add -3 to each side,

-4 < -5m < 0

Divide each side by -5,

4/5 > m > 0 (Attn: When you divide by a negative number, you have to switch the direction of inequality sign.)

Graph 0 and 4/5 on a number line each with a small circle and draw a segment linking the two circles. You are done!