Writing and using inequalities | Linear inequalities | Algebra I | Khan Academy
Writing and using inequalities | Linear inequalities | Algebra I | Khan Academy

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!

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost \$2 and earrings cost \$3. She needs to make at least \$500.

Step 1: Highlight the important information in the problem.

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost \$2 and earrings cost \$3. She needs to make at least \$500.

Step 2: Identify your variables. Think about what you don’t know and need to know to solve the problem.

Let x = the number of bracelets sold.

Let y = the number of earrings sold.

Step 3: Write an inequality to represent the income form the jewelry sold.

2x + 3y > 500

Here’s how I came up with this inequality.

Step 4: Sarah knows that she will sell more than 50 bracelets. Write an inequality to represent this situation.

x > 50

Step 5: Graph the two inequalities and shade the intersection.

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.

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