6th Grade Math Textbook, Fundamentals

 &KDSWHU

3-1

Inequalities

Objective To identify and use inequality symbols •To express inequalities as

word sentences • To express word sentences as inequalities • To determine if a value

makes an inequality true or false

Tina travels by car across the country. Her car can get
as much as 36 miles per gallon of gas on the highway.
How can you express the number of miles per gallon
of gas Tina’s car can get on a highway as an inequality?

An is a mathematical sentence that

compares two expressions using , , , , or.

To represent “as much as 36 miles per gallon,”

use the inequality symbol foris less than or equal to,.

Let xthe car’s gas mileage.

x 

36 Read as: xis less than or equal to 36.

Inequalities can be written as word sentences.

Word sentences can be written as inequalities.Word Sentence Inequality

Inequalities with variables are called.

Open sentences are neither true nor false. When a value is substituted

for the variable, the inequality becomes a closed sentence.

Once a value has been substituted for a variable, you can determine

whether the inequality is true or false:

• If the closed sentence is true, the inequality is true
  for that value of the variable.


• If the closed sentence is false, the inequality is false
  for that value of the variable.

open sentences

inequality

inequality

Key Concept

Inequality Symbols

is less than

is greater than

is not equal to

is less than or equal to

(^) is greater than or equal to



Remember:Closed sentences
are either true or false.
Inequality Word Sentence
c |6|  7 A number, c, minus the absolute value of negative 6 is less than7.
b 8 A number, b, is greater than or equal to8.
 6
c
2 A number, c, divided by 2 is not equal to6.
n
4 A number, n, is less than or equal to4.
Word Sentence Inequality
A number, d, plus negative three is greater thanfive. d(3)  5
A number, n, squared is less than or equal tofour. n^2
4
Ben runs no more than6 miles each day. Let mmiles run. m 6 mi
Half the cost of a pizza is more than$5. Let pcost of pizza. $5
p
2
Jasmine rides her bike at a speed of at least15 miles per hour.
Let xJasmine’s speed. x^ 15 mi/h