Inequalities
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Inequalities. Because “ I<3U ” does not mean “ I love you. ” Mathematically, it means I less than 3 of you. What is an inequality?. Mathematical sentence that compares quantities. To solve an inequality you have to find values for the variable that make the sentence true.

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Inequalities

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Inequalities

Inequalities

Because “I<3U” does not mean “I love you.” Mathematically, it means I less than 3 of you.


What is an inequality

What is an inequality?

  • Mathematical sentence that compares quantities.

  • To solve an inequality you have to find values for the variable that make the sentence true.

  • Inequalities do not contain equal signs.


Inequality symbols

Inequality symbols


Translating sentences to inequalities

Translating sentences to inequalities

  • TIPS

    • Use a variable to represent the unknown

    • Look for key words to determine the inequality symbol you will use.

  • Example 1:

We don’t know what the number is. We will use x to represent the unknown number.

is greater than

2.

A number

x > 2


More examples

More Examples

We don’t know what the number is. We will use x to represent the number.

  • Example 2:

  • Example 3:

The maximum

value of a number

is 28.

x ≤ 28

We don’t know what the number is. We will use x to represent the number.

A number is

greater than or equal to

four.

x ≥ 4


Graphing inequalities

Graphing inequalities

  • Steps:

    • Draw a number line and place the number in the problem in the middle of the number line.

    • Fill in numbers on the number line.

    • Put a circle on the number 2 on the number line.

      • For this example, you leave the circle open (not colored in).

    • Shade in the part of the number line that shows the numbers that are greater than 2.

  • Example 1:

    x > 2

0 1 2 3 4


Examples with graphing inequalities

Examples with Graphing Inequalities

-Both of these examples mean that the variable can be equal to the number in the inequality.

-When you graph these inequalities, color in the circle.

Example 2:

x ≤ 28

Example 3:

x ≥ 4


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