Inequalities · Meet inequalities · 1.2

Words to inequalities.

To turn a sentence into an inequality, let x stand for the unknown number, pick the symbol from the phrase, and write the number. “A number is at least 5” becomes x ≥ 5.

01 / THE IDEA

See it work.

Watch the method

Words to inequalities

“A number is at least 5” → x ≥ 5.

1 / 1
a number is at least 5\text{a number is at least 5}
1

Translate the phrase

Pick the symbol, then write x and the number.

x≥5x ≥ 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

Type the solution, e.g. x < 4 (you can write <= for ≤).

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— / WHY IT WORKS

The idea underneath.

Build the inequality

x on the left, the matching symbol, then the value.

Why it works

Say it, then symbol it.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write this as an inequality (use x): “a number is at most 6”.

1

Translate the phrase

Pick the symbol, then write x and the number. x ≤ 6

EX 2medium

Write this as an inequality (use x): “a number is at least 6”.

1

Translate the phrase

Pick the symbol, then write x and the number. x ≥ 6

EX 3hard

Write this as an inequality (use x): “a number is less than 10”.

1

Translate the phrase

Pick the symbol, then write x and the number. x < 10

04 / COMMON TRAPS

Where students slip.

Trap

Flipping the symbol direction.

Fix

“More than 5” is x > 5, not 5 > x written backwards.

Trap

Using = instead of an inequality.

Fix

These phrases are open-ended ranges, not single values.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Write this as an inequality (use x): “a number is at least 6”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
C2

Write this as an inequality (use x): “a number is less than 8”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
C3

Write this as an inequality (use x): “a number is more than 9”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
C4

Write this as an inequality (use x): “a number is more than 9”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
Apply

Apply (4)

A1

Write this as an inequality (use x): “a number is less than 4”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
A2

Write this as an inequality (use x): “a number is more than 5”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
A3

Write this as an inequality (use x): “a number is at most 3”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
A4

Write this as an inequality (use x): “a number is at least 3”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
Extension

Extension (4)

E1

Write this as an inequality (use x): “a number is at least 6”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
E2

Write this as an inequality (use x): “a number is more than 7”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
E3

Write this as an inequality (use x): “a number is at most 3”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.
E4

Write this as an inequality (use x): “a number is less than 8”.

Need a hint?
  • Pick the symbol from the phrase.
  • Write x, the symbol, then the number.