SOL Objective(s):
7.15 The student will
a) solve onestep inequalities in one variable; and
b) graph solutions to inequalities on the number line.
8.15 The student will
b) solve twostep linear inequalities and graph the results on a number line.
a) solve onestep inequalities in one variable; and
b) graph solutions to inequalities on the number line.
8.15 The student will
b) solve twostep linear inequalities and graph the results on a number line.
Previous and Related SOL Objectives6.20 The student will graph inequalities on a
number line. 
Prerequisite SkillsSolve equations
Knowledge of properties 
Khan Skill PhrasesInequalities on a Number Line
OneStep Inequalities TwoStep Inequalities MultiStep Linear Inequalities 
The Basics and Background Information
• A onestep inequality is defined as an inequality that requires the use of one operation to solve (e.g., x – 4 > 9)
• The inverse operation for addition is subtraction, and the inverse operation for multiplication is division.
• When both expressions of an inequality are multiplied or divided by a negative number, the inequality symbol reverses (e.g., –3x < 15 is equivalent to x > –5).
• Solutions to inequalities can be represented using a number line.
• A twostep inequality is defined as an inequality that requires the use of two different operations to solve (e.g., 3x – 4 > 9).
• The inverse operation for addition is subtraction, and the inverse operation for multiplication is division.
• When both expressions of an inequality are multiplied or divided by a negative number, the inequality symbol reverses (e.g., –3x < 15 is equivalent to x > –5).
• Solutions to inequalities can be represented using a number line.
• A twostep inequality is defined as an inequality that requires the use of two different operations to solve (e.g., 3x – 4 > 9).
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Represent and demonstrate steps in solving inequalities in one variable, using concrete materials, pictorial representations, and algebraic sentences.
• Graph solutions to inequalities on the number line.
• Identify a numerical value that satisfies the inequality.
• Solve twostep inequalities in one variable by showing the steps and using algebraic sentences.
• Graph solutions to twostep linear inequalities on a number line.
• Represent and demonstrate steps in solving inequalities in one variable, using concrete materials, pictorial representations, and algebraic sentences.
• Graph solutions to inequalities on the number line.
• Identify a numerical value that satisfies the inequality.
• Solve twostep inequalities in one variable by showing the steps and using algebraic sentences.
• Graph solutions to twostep linear inequalities on a number line.
Vocabulary and Things to Know:

Be Able To:

The topic: What is it and what will we learn?
Inequalities work much the same way equations do, with one exception, and have multiple solutions.
Equations and InequalitiesWhile the title of this KhanAcademy video is Equations and Inequalities, the inequality portion is the first 9 minutes. Sal starts off by showing how to translate word problems into inequalities, and then goes on to show examples of checking to see if given solutions are true for corresponding inequalities by substituting solutions and then simplifying. At the 9 minute mark, he shares an example of translating a word problem into an equation, and then goes on to share another multistep inequality word problem.


Learn ZillionThis website provides text and a video that demonstrates solving a twostep inequality using inverse operations. They use some unnecessary horizontal lines in instruction, but it is a good model of basics.
The second link provides instruction on graphing inequalities. I'm not sure if these are viewable, as it asked me to make an account, but if you're able to see it, it's a good basic tutorial. 
Math WarehouseThis website provides text information, an interactive grapher, and examples of graphing inequalities (simply scroll down to see them).

Math Worksheets 4 KidsThis link provides worksheets with answers on solving inequalities, as well as graphing from inequalities and writing inequalities from graphs. Worksheets are differentiated by levels of difficulty.

MathAids.comThis link enables you to create your own worksheets.
