x 3 x + 3 = 8 Come play with numbers!
Word problems

Can a sentence become an equation?

# Story → equation 1. Choose a letter for the unknown 2. Translate words 3. Write `=` 4. Solve 5. Check in the **story**, not only in the algebra ## Word bank - sum → + - difference → − - product → × - quotient → ÷ - “is” / “gives” / “makes” → = - “2 more than x” → `x + 2` - “2 less than x” → `x − 2` - “twice x” → `2x` ## Example “A number plus 8 is 20.” `x + 8 = 20` → `x = 12` ## Five beats of a word problem 1. **Name** — Let x be the unknown (say what it is). 2. **Translate** — each phrase becomes maths. 3. **Equals** — find the word that means =. 4. **Solve** — one-step or two-step, as usual. 5. **Story-check** — put the number back into English. ### Word bank (copy this) | English | Maths | | --- | --- | | sum, more than, plus, increased by | + | | difference, less than, minus, decreased by | − | | product, times, twice, thrice | × | | quotient, shared, per | ÷ | | is, gives, makes, equals, will be | = | ### “Less than” is the slippery one “2 less than x” = `x − 2` “2 less than 10” = 8, which is 10 − 2, not 2 − 10.

By the end of this lesson

Translate a short English sentence into an equation, solve it, and check in the story.

Remember

  • Choose a letter and write what it stands for in a sentence.
  • sum → + · difference → − · product → × · “is/gives/makes” → =.
  • “2 more than x” is x + 2. “2 less than x” is x − 2. “twice x” is 2x.
  • Solve with the methods you already have.
  • Check in the story, not only in the algebra (“does 12 plus 8 really make 20?”).

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Plus is

“A number plus 8 is 20.”

  1. Let x be the number.
  2. x + 8 = 20
  3. x = 12
  4. Story check: 12 + 8 = 20 ✓

Answer: x = 12

Example 2 — Twice

“Twice a number is 18.”

  1. 2x = 18
  2. x = 9
  3. Twice 9 is 18 ✓

Answer: x = 9

Example 3 — Less than

“2 less than a number is 11.”

  1. x − 2 = 11 (start from the number, take 2 away)
  2. x = 13
  3. 13 − 2 = 11 ✓

Answer: x = 13

Check: Not 2 − x unless the sentence says “2 minus the number”.

Common mistakes

Slip “2 less than x” written as 2 − x.

Fix It is x − 2.

You start with x and remove 2.

Slip Skipping “let x be…”.

Fix If you do not name x, you will lose what the number means.

One short sentence.

Slip Checking only x = 12 and not “12 plus 8 is 20”.

Fix The story is the real-world check.

Both checks are good; the story one catches a wrong setup.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

1. “A number minus 5 is 9.” Equation?

Answer: x − 5 = 9

2. Then x =

Answer: 14

3. “Three times a number is 24.” x =

Answer: 8

4. “A number plus 6 is 6.” x =

Answer: 0

Touch practice

9 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

Word problems in exams and life.

Connect

Requirements become code.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

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