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

-1<3-5m<3

4.9 4.9 (233 lesson ratings) (233)
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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 :)

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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- 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

Mike C. | Enthusiastic Tutor for Middle and High School StudentsEnthusiastic Tutor for Middle and High S...
4.8 4.8 (82 lesson ratings) (82)
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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.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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Solve first,