Neft Teacher · Learn It

Unit 8 · Standard 6.AT.9

Write and Represent Inequalities

Lesson 8-4 · Learn It — how the math works

Why we're learning this

Detective Navarro is narrowing down suspects. A witness says the suspect is at least 18 years old. The detective writes the inequality a ≥ 18, where a is the suspect's age. How does this help eliminate suspects?

✱ Math Workbench

Learn It

How do I write an inequality from words?

An inequality compares two amounts using <, >, ≤, or ≥. I use one when many values are allowed, not just one. I pick a variable and match the words to the right symbol.

Picture itSee what the math looks like before you read about it

Three balance scales are shown. On two of them the pans hang at different heights, so one side is heavier. On the third the pans are level.
Where you see this in real lifeThree balance scales are shown. On two of them the pans hang at different heights, so one side is heavier. On the third the pans are level.

Watch me solve itI do — read one step at a time

The problem looks like this
Number line: a closed circle at 18 with a ray pointing right shows a ≥ 18, so a can be 18, 19, 20, and up.141516171819202122232418
  1. Clue: 'The suspect is at least 18 years old.'
  2. I let a stand for the age. 'At least 18' means 18 or more.
  3. 'At least' includes 18, so I use the symbol ≥.
  4. My is a ≥ 18. So a could be 18, 19, 20, and up.

Watch out — mistakes students make here

  • 'At least' includes 14 — you need the 'or equal to' line.
  • 'At least' means 14 or more, so the arrow points the other way.
  • 'At least 14' means 14 or greater, not less than.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Clue: 'A bag holds fewer than 10 items.' What does 'fewer than' mean?
  2. It means , and it does NOT include 10, so we use <.
  3. We let n be the number of items: n < 10.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Sort the phrase cards into the matching symbol: >, <, ≥, or ≤.
  • Then for the practice situations.

Solve: A parking garage charges if your stay is more than 2 hours. Which represents times t that are charged?

My answer

Stuck? Open one hint at a time.

Hint 1

The charge starts once the stay goes PAST 2 hours. Is a stay of exactly 2 hours charged?

Hint 2

If exactly 2 hours is NOT charged, the boundary is excluded — that rules out any symbol with the 'or equal' bar.

Hint 3

Test t = 2 and t = 3: only stays longer than 2 are charged. Pick the symbol that makes t = 3 true but t = 2 false.

Check my answer
✅ Answer: t > 2
'More than 2 hours' means strictly greater than: t > 2. Exactly 2 hours is not charged.

Turn & TalkSay it out loud with a partner

A witness says the suspect is 'at least 18 years old,' written as a ≥ 18. Why does the detective use an here instead of an equation like a = 18?

Try starting with:

  • An inequality fits better than an equation because ___.Una desigualdad encaja mejor que una ecuación porque ___.
  • 'At least 18' means the age can be ___.'Al menos 18' significa que la edad puede ser ___.
Use these wordsinequalitygreater thanless thanat least / at most