PSAT Math : How to graph an inequality with a number line

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Graph An Inequality With A Number Line

What property of arithmetic is demonstrated here?

If  and , then .

Possible Answers:

Commutative

Transitive

Associative

Symmetric 

Inverse

Correct answer:

Transitive

Explanation:

The symbols express the idea that if a number is less than a second number, which is less than a third, then the first number is less than the third. This is the transitive property of inequality.

Example Question #1 : Number Line

On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?

Possible Answers:

10

18

-18

4

Correct answer:

18

Explanation:

The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.

|14- (-4)| = |14+4| = |18| = 18

Example Question #8 : Integers

Which of the following is a graph for the values of  defined by the inequality stated above?

Possible Answers:

Ineq23

Ineq24

Ineq22

Ineq25

Ineq21

Correct answer:

Ineq21

Explanation:

To begin, you must simplify so that you "isolate" , (i.e. at least eliminate any coefficients from it). To do this, divide all of the members of the inequality by :

Now, this inequality represents all of the numbers between 13 and 32.  However, it does include  (hence, getting a closed circle for that value) and does not include  (hence, getting an open circle for that value). Therefore, it looks like:

Ineq21

Example Question #2 : How To Graph An Inequality With A Number Line

Ineq3

Which of the following inequalities is represented by the number line shown above?

Possible Answers:

Correct answer:

Explanation:

Since the inequality represents one range of values between two end points (both of which are included, given the sign being "less than or equal"), you know that whatever you answer, it must be convertible to the form:

Now, you know that it is impossible to get this out of the choices that have no absolute values involved in them. Therefore, the only options that make sense are the two having absolute values; however, here you should choose only the ones that have a , for only that will yield a range like this. Thus, we can try both of our options.

The wrong answer is simplified in this manner:

And you can stop right here, for you know you will never have  for the left terminus.

The other option is simplified in this manner:

This is just what you need!

Example Question #3 : How To Graph An Inequality With A Number Line

Which of the following is a graph for the values of  defined by the inequality stated above?

Possible Answers:

Ineq13

Ineq11

Ineq15

Ineq14

Ineq12

Correct answer:

Ineq11

Explanation:

Begin by solving for :

Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:

Ineq11

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: