6th Grade Math Textbook, Fundamentals

 &KDSWHU

3-2

Graph Inequalities on a Number Line

Objective To use a replacement set to identify the solution set of an inequality • To graph the

solution set of an inequality on a number line • To write an inequality that describes a given graph

Pete scored at least92 points out of 100 points on his
science test. If test scores are whole numbers, what is
the range of possible test scores Pete might have
received on his science test?

To find the range of possible test scores, write

an inequality and identify the solution set as a

specific part of the replacement set.

Let xPete’s possible test score.

x 92

A , R, is a set of numbers to be used as

possible values for the variable in an equation or inequality.

Sometimes you may be told what the replacement set is.

R{0, 1, 2, 3, ... 100}

A , S, contains all the values for the variable that make

the equation or inequality true.

S{92, 93, 94, 95, 96, 97, 98, 99, 100}

So the range of test scores that Pete might have received is 92–100.

You can graph the solution set

of the inequality on a number line.

The solution set for an inequality can be one, some, all, or none of the values

in the replacement set.

solution set

replacement set

Think

at least92 points means

92 or more points.

The replacement setfor the test scores is the

set of whole numbers from 0 to 100.

The solution setfor the test scores is the

set of whole numbers from 92 to 100.

Inequality Replacement Set Solution Set

y 25 {24, 25, 26, ...} {24}

x 8 {0, 1, 2, 3, ...} {9, 10, 11, 12, ...}

x 

8 {4, 5, 6, 7, ...} {4, 5, 6, 7, 8}

t 10 {3, 2, 1, 0, 1, 2, ...} {10, 11, 12, 13, ...}

t 

10 {..., 8, 9, 10} {..., 8, 9, 10}

a 0 {0, 1, 2, 3, ...} { } or.

When nonumber from the replacement set makes the

inequality true, the solution set is the empty set, { } or.

90 91 92 93 94 95 96 97 98 99 100