Main content

## SAT

### Course: SAT > Unit 6

Lesson 3: Heart of Algebra: lessons by skill- Solving linear equations and linear inequalities | Lesson
- Understanding linear relationships | Lesson
- Linear inequality word problems | Lesson
- Graphing linear equations | Lesson
- Systems of linear inequalities word problems | Lesson
- Solving systems of linear equations | Lesson
- Systems of linear equations word problems | Lesson

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Linear inequality word problems | Lesson

## What are linear inequality word problems, and how frequently do they appear on the test?

**Linear inequalities**are very common in everyday life. While a linear equation gives us exactly one value when solved, a linear inequality gives us multiple values. The table below shows a couple of statements, their inequalities, and possible solutions.

Statement | Inequality | Possible solutions |
---|---|---|

"It'll take at least 30 minutes to get downtown." | x, is greater than or equal to, 30 | 30 minutes, 45 minutes, etc. |

"I wouldn't pay more than dollar sign, 6 for a sandwich!" | x, is less than or equal to, 6 | dollar sign, 4, dollar sign, 5, point, 50, etc. |

On your official SAT, you'll likely see

**1 to 2 questions**that test your ability to write and solve linear inequalities.This lesson builds upon an understanding of the following skills:

**You can learn anything. Let's do this!**

## How do I write linear inequalities based on word problems?

### Using inequalities to solve problems

### Linear inequality word problems

It may not be hard to translate "it takes at least 30 minutes to get downtown" into a linear inequality, but some SAT word problems are several sentences long, and the information we need to build an inequality may be scattered around.

#### What are some key phrases to look out for?

The table below lists some common key phrases in inequality word problems and how to interpret them.

**Note:**c is a constant in the examples.

Phrase | Translates to... |
---|---|

"More than c", "greater than c", or "higher than c" | is greater than, c |

"Less than c" or "lower than c" | is less than, c |

"Greater than or equal to c" or "at least c" | is greater than or equal to, c |

"Less than or equal to c" or "at most c" | is less than or equal to, c |

"No less than c" | is greater than or equal to, c |

"No more than c" | is less than or equal to, c |

"Least", "lowest", or "minimum" value | The smallest value that satisfies the inequality |

"Greatest", "highest", or "maximum" value | The largest value that satisfies the inequality |

"A possible" value | Any value that satisfies the inequality |

#### Let's look at some examples!

Ari can harvest at least 48 pounds of honey from her bee colony. If she wants to package the honey harvest in 1, point, 5-pound jars, what is the minimum number of jars she can fill?

Bryan wants to make for his friends. The snack is made by inserting a peppermint stick into the middle of a pickle. If a peppermint stick costs dollar sign, 0, point, 40 and a pickle costs dollar sign, 2, point, 30, what is greatest number of peppermint stick pickles Bryan can make if he has dollar sign, 20 to buy the ingredients?

### Try it!

## Your turn!

## Things to remember

Phrase | Translates to... |
---|---|

"More than c", "greater than c", or "higher than c" | is greater than, c |

"Less than c" or "lower than c" | is less than, c |

"Greater than or equal to c" or "at least c" | is greater than or equal to, c |

"Less than or equal to c" or "at most c" | is less than or equal to, c |

"No less than c" | is greater than or equal to, c |

"No more than c" | is less than or equal to, c |

"Least", "lowest", or "minimum" value | The smallest value that satisfies the inequality |

"Greatest", "highest", or "maximum" value | The largest value that satisfies the inequality |

"A possible" value | Any value that satisfies the inequality |

## Want to join the conversation?

- Hi

Cristian's goal is to walk an average of 50 kilometers

The question does not mention "at least"(6 votes)- Because all of the answer choices only have a greater than or equal to sign and to meet a goal you can either be exactly at the threshold or even exceed it, you can infer that the question wants you to have a greater than or equal to inequality.

Your concern's definitely valid though, and I think a question on the real SAT would be a little more concrete, saying something like "Cristian's goal is to walk at least an average of 50 kilometers".(14 votes)

- wanted to practice more question about linear inequalities word problem(3 votes)
- did we have an essay on sat in 2023? and not or optional does it cover our overall marks?(2 votes)
- The SAT essay was removed in June 2021. As of writing, (April 2023), there is no essay section on the SAT, and the same goes for its digital redesign. Prior to this, the SAT essay was optional and was scored completely separately, but now it's been removed altogether.(2 votes)

- shouldn't the minimum no. of jars she could fill be 0?(1 vote)
- No , try to read the question more carefully(2 votes)

- What is difference between SAT and LCAT (LUMS Common Admission Test)? I mean,to what extent do they differ?(0 votes)
- They are the same. Both have the same format. The SAT is an international test while LCAT was actually made for local students who couldn't take the SAT or just can't afford to.(2 votes)