how do i graph x < 4and x > 6 on a number line?

Question

This is an inequality and a graph

Answer 1

The easiest way to do this is to draw the boundaries and just color where it is true.  I feel Matthew's pain drawing this one out...

On a axis:

                       |
_____________|__________________________  x=6
____________  |__________________________  x=4
                       |
                       |
-----------------------------------------------------
                       |
                       |

What region is x<4 AND x<6? Anywhere below the x=4 and above x=6.

 

Answer 2

Great question!  When you are graphing compound inequalities, it's very important to note whether the word joining them is "AND" or "OR".  When using "or", the solutions are any values that satisfy AT LEAST ONE inequality. Sometimes this looks like two arrows going separate directions. With "and", any solutions must satisfy BOTH inequalities.  Sometimes this looks like a line segment.

In your example x<4 and x>6, you want solutions that are both less than 4 and greater than 6.  But no such numbers exist!  If you had x<4 and x<6, then your solution would be all numbers less than 4 (since all numbers less than 4 are also less than 6).  However, in your example, there are no such numbers that satisfy both.  Therefore, there is no solution.  On a number line, this looks like an empty number line.

Let me know if you need clarification!  It's easier to visualize with drawing than text, but I hope this was enough of an explanation with just words.  :)

Answer 3

Picture a number line... or see if I can draw one here: <-- -infinity ... -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ... +infinity --> "x<4" means all numbers less than 4, and does not include the number 4 itself. Similarly, "x>6" means all numbers greater than 6, and, again, does not include the number 6 (if it did, it would say "x>=6"). To indicate the exclusion of 4 and 6, use an open circle. Then draw a continuous line from the open circle above 4 and continue it left, then do the same thing from 6 to the right. ---------------------------------------o o------------------------------ <-- -infinity ... -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ... +infinity -->