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## Algebra 1

### Course: Algebra 1 > Unit 7

Lesson 3: Modeling with linear inequalities- Writing two-variable inequalities word problem
- Solving two-variable inequalities word problem
- Interpreting two-variable inequalities word problem
- Two-variable inequalities word problems
- Modeling with systems of inequalities
- Writing systems of inequalities word problem
- Solving systems of inequalities word problem
- Graphs of systems of inequalities word problem
- Systems of inequalities word problems
- Graphs of two-variable inequalities word problem
- Inequalities (systems & graphs): FAQ
- Creativity break: What can we do to expand our creative skills?

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# Inequalities (systems & graphs): FAQ

Frequently asked questions about systems and graphs of inequalities

## Why do we need to learn how to check solutions of two-variable inequalities?

We need to learn this skill in order to verify whether or not a given coordinate point satisfies an inequality. Checking solutions is essential for being able to graph inequalities and model real-life situations with them.

Practice with our Solutions of inequalities: algebraic exercise.

Practice with our Solutions of inequalities: graphical exercise.

## What are some real-world applications of linear inequalities?

Linear inequalities can be used in a variety of real-world contexts. For example, they can be used to model constraints for a manufacturing company or to create a budget in personal finance. They can also be used to solve optimization problems or analyze data sets.

Practice with our Two-variable inequalities word problems exercise.

## How do we graph two-variable inequalities?

There are a few steps to graphing two-variable inequalities. First, we graph the corresponding equation as if it were an equality. Then we use a test point to determine which side of the line we should shade in order to represent the inequality. Finally, we show whether or not the line itself is included in the solution set by drawing it as a solid or dashed line.

Practice with our Graphs of inequalities exercise.

## How do we graph a system of linear inequalities?

When graphing a system of linear inequalities, we follow the same process we do for graphing a single inequality, but we have to do it multiple times. For each inequality in the system, we graph the corresponding equation as an equality, determine which side of the line to shade, and decide whether to draw a solid or dashed line. Once we have graphed all of the inequalities, the solution set is the region where all of the shaded regions overlap.

Practice with our Systems of inequalities graphs exercise.

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