# Thread: inequality graph

1. ## inequality graph

what is the graph of 1/x < 4 , where x belongs to real no. , also find the intervals for which above inequality is true ?
how can we relate these intervals with the graph ?

2. Originally Posted by kashif shah
what is the graph of 1/x < 4 , where x belongs to real no. , also find the intervals for which above inequality is true ?
how can we relate these intervals with the graph ?
Follow the standard procedure for solving rational inequalities:

Move everything over to one side of the inequation:

. . . . .$\displaystyle \frac{1}{x}\, -\, 4\, <\, 0$

Combine the two terms into one rational-expression fraction:

. . . . .$\displaystyle \frac{1\, -\, 4x}{x}\, <\, 0$

Find the x-values for which each of the numerator and denominator is equal to zero. These split the number line into intervals (three intervals, in this case). Then check the sign on each interval.

To learn how to graph the solutions to inequalities (that is, how to mark the solution intervals on the number line), try here. (The lesson teaches how to solve linear inequalities, but that's the first type that students usually study, so that's when the basic terms and notation are customarily covered.)

3. Hello Kashif Shah:
Let me illustrate an answer with the graph.
The graph cuts at $\displaystyle x=1/4$

Hope this helps