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Systems of InequalitiesWord Problems

As you get further into Algebra 1, you will find that the real world problems become more complex. They have more questions to be answered and require more steps to find the solution.

When you get into systems of inequalities, this is especially true because you are dealing with two inequalities.

But... don't let that intimidate you! You have all the skills that you need to solve these problems. Take one step at a time and think about what you need in order to answer the question. Read through my example very carefully, and study how I performed each step. Pay careful attention to the key words (highlighted words) and how each inequality was written based on the problem.

Then complete the practice problems. You can do it!

Example 1

For most real world problems, it will be easiest to graph the inequalities using the x and y intercepts. Make sure that you scale your grid so that both inequalities can be graphed on the same grid.

Steps for Solving a System of Inequalities Word Problem

• Read the problem and highlight important information.

• Identify the variables.

• Find one piece of information in the problem that you can use to write an inequality.

• Find a different piece of information that you can use to write a second inequality.

• Graph both inequalities on a grid. Make sure you use appropriate boundary lines and shade the correct half plane for each inequality.

• Identify the intersection of the two inequalities and answer the questions that pertain to the problem.

Now it's time to move onto the practice problems. You can do it!

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