Let’s take a look at how to solve inequality word problems. You’ll need to be able to recognize inequalities that reflect the context described in a word problem.

To solve these types of questions, you should be familiar with phrases such as less than, more than, at least, etc.

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Below this lesson, you will find a list of the most popular phrases that appear in inequalities-related word problems.

It’s important that you pay attention to the wording of the question so that you know exactly what you’re being asked.

Once you understand that, the math needed is not necessarily complex.

**Let’s check this example.
**

Sharon is selling earrings and bracelets to make some money for her summer vacation. Her bracelets are $2 each and her earrings are $3 each. Sharon needs to make no less than $500. Now, write a mathematical inequality that represents the income Sharon’s sold jewelry.

**Step 1**: Highlight the important information in the problem.

Sharon is selling earrings and bracelets to make some money for her summer vacation. The bracelets are $2 each and her earrings are $3 each. Sharon needs to make no less than $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:** Now, write your inequality that represents Sharon’s income from her sold jewelry.

2x + 3y is greater or equal to (≥) 500.

Let’s see how we came to this inequality:

$2 times the number of bracelets

plus $3 times the number of earrings

is greater or equal to 500 because Sharon needs at least $500. At least 500, has the same meaning as “greater or equal to” 500, therefore we used this (≥) symbol. As you see solving word problems with inequalities is not difficult when you translate words into a math equation. That’s it. Now it’s your turn. Let’s solve a few quizzes.

## Inequality Word Problems Keywords

More than, greater than | Inequality, > |

At least, minimum, greater than, or equal | Inequality, ≥ |

Fewer than, less than | Inequality, < |

At most, maximum, less than, or equal | Inequality, ≤ |