How do you draw inequalities which are fractions?

Answer 1

Do you mean how does one express inequalities using fractions? Just write out the fractions as you would normally and then use one of the appropriate inequality signs, >, >=, <, <=.

Examples:

1/2 > 1/3 because 0.50 is larger than 0.33.

But -1/2 < -1/3 ** because -1/2 lies farther to the left of the origin, or is more negative, than -1/3. Convert them to decimal form, and you see that -0.50 is smaller than -0.33.

Other examples:

7/8 > 3/4, 1/6 < 1/5, -1/5 > -1/4.

One can also introduce variables into the fractions. Such as:

(1/2)x >= 3/5 --> x >= (3/5)(2) --> x >= 6/5.

Watch out for division or multiplication by a negative number however. As you can see from the inequality above marked ** either of those operations reverses the direction of the inequality sign. Which operation did we perform there, division or multiplication by a negative number? Or perhaps both? That's something to ponder. Hint: Try dividing and multiplying a number by negative one and see what results you obtain. Then ask yourself whether they are different or the same.

I'm sure by now you get the idea.

Answer 2

To answer your question, it's better to start with a specific example x > 3/4.

On a number line, you separate the segment from 0 to 1 into four equal parts. Then all the domain after the third part is x > 3/4.