Lesson 8.4Representing Inequalities
Start hereWords, worked example, and sentence starters
Learning target I can write inequalities to represent real-world situations.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| InequalitySpanish: Desigualdad | A math sentence that compares two sides with <, >, ≤, or ≥. | x > 5 means x can be 6, 7, 8, ... — any number greater than 5 |
| Greater thanSpanish: Mayor que | The > sign, showing one number is bigger. | 8 > 3 — eight is larger than three |
| Less thanSpanish: Menor que | The < sign, showing one number is smaller. | less than 7 → x < 7 |
| At least / At mostSpanish: Al menos / A lo más | 'At least' means ≥. 'At most' means ≤. | 'At least 10 players' → p ≥ 10 (could be 10, 11, 12, ...); 'At most 5 tries' → t ≤ 5 (could be 5, 4, 3, ...) |
| VariableSpanish: Variable | A letter that stands for a number that is unknown or can change. | In x > 5, the letter x stands for any number greater than 5. |
| No more thanSpanish: No más de | A phrase meaning less than or equal to (≤). | no more than 7 |
How it worksWorked examplewriting an inequality and plotting solutions
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A backpack rule says a student may carry no more than 15 pounds. Show the weights that are allowed.
- Name the variable: let w = the pounds in a student's backpack.
- The phrase 'no more than' allows 15 itself and every weight below it.
- That phrase matches ≤, so write w ≤ 15.
- Draw a number line near 15 and plot 15, 12, and 9 — each one is allowed.
Answer: w ≤ 15, so any weight of 15 pounds or less is a solution.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A small ferry carries at most 40 passengers. Write an inequality and show some solutions.
- Name the variable: let p = .
- 'At most' means p can be equal to 40 or than 40.
- Write the inequality: p 40
- Draw a number line and plot three values that work: , ,
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The phrase tells me the symbol is .
- My inequality is because the limit is .
- On my number line I marked because .
- The value (is / is not) a solution because .
Word bank inequalityat mostno more thanless thanlimitsymbolnumber lineplotboundarysolutionrangevariable
Watch outA common mistake
A common mistake in Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value. For 'the suspect is at least 18 years old,' students often write a > 18 instead of the correct a ≥ 18 — this wrongly excludes 18 itself, even though 'at least 18' means 18 counts as a match. The same error happens in reverse with 'at most': for 'the getaway bag holds at most 12 items,' students write n < 12 instead of n ≤ 12. Always ask: does the key phrase include the number ('at least,' 'at most,' 'no more than,' 'no fewer than' → use ≥ or ≤) or exclude it ('more than,' 'fewer than' → use > or <)?
Lesson 8.4Representing Inequalities
Apply Day · Version ASupported practice
Learning target I can write inequalities to represent real-world situations.
-
1Complete each step, then write the final answer.
You must be at least 13 to see a movie. Which symbol goes in the box for the age a: a ☐ 13?
Show your workHint "At least 13" means 13 or more. Is 13 included?
Final answer: -
2Complete each step, then write the final answer.
A pencil box holds fewer than 24 pencils. Which symbol goes in the box: p ☐ 24?
Show your workHint "Fewer than 24" means less than 24. Is 24 included?
Final answer: -
3Complete each step, then write the final answer.
A sign says: "At most 6 people in the room." Which symbol goes in the box: p ☐ 6?
Show your workHint "At most 6" means 6 or less. Is 6 included?
Final answer:
Lesson 8.4Representing Inequalities
Apply Day · Version BCore practice
Learning target I can write inequalities to represent real-world situations.
-
1Complete each step, then write the final answer.
A team needs at least 10 players. Tom writes s > 10. Is he right? Which symbol should go in the box: s ☐ 10?
Show your workFinal answer: -
2Complete each step, then write the final answer.
An elevator can carry a maximum of 1,500 pounds. Which symbol goes in the box: w ☐ 1,500?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A bag can hold at most 25 pounds. Which symbol goes in the box: w ☐ 25?
Show your workFinal answer:
Lesson 8.4Representing Inequalities
Apply Day · ChallengeExtension
Learning target I can write inequalities to represent real-world situations.
-
1Circle the letter of the best answer. Show how you know.
A fair ride requires each rider to be at least 48 inches tall. Let h be a rider's height in inches. Which inequality represents the heights that are allowed to ride?
- Ah ≥ 48
- Bh > 48
- Ch ≤ 48
- Dh < 48
Show your work -
2Complete each step, then write the final answer.
Clue: "The suspect is not taller than 70 inches." Which symbol goes in the box for the height h: h ☐ 70?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A pool is open to swimmers no younger than 7. Which symbol goes in the box for a swimmer's age a: a ☐ 7?
Show your workFinal answer: