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

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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!