# Two steps, reverse order
Think of dressing: socks then shoes.
To undo: shoes off **first**, then socks.
If someone did: **multiply by 2, then add 3**
`2x + 3 = 11`
Undo in reverse:
1. Subtract 3 → `2x = 8`
2. Divide by 2 → `x = 4`
## Why reverse?
The last thing done to x is “+ 3”. Peel that layer first.
> PEMDAS builds the expression. Solving **unwraps** it, like opening a gift from the outside.
## Dressing and undressing
To dress: socks, then shoes.
To undress: shoes first, then socks.
If someone built `2x + 3`:
1. Take x
2. Multiply by 2
3. Add 3
You undo 3, then undo 2.
### The shape to recognise
`ax + b = c`
or `ax − b = c`
or `x/a + b = c`
Outside number (`b`) first, then the multiply/divide.
### Write it like this every time
```
2x + 3 = 11
2x + 3 − 3 = 11 − 3
2x = 8
x = 4
Check: 2(4)+3 = 11
```
Why peel the last layer first?
By the end of this lesson
Name the last operation done to x and undo it first, then undo the remaining one-step.
Remember
- A two-step equation wraps x in two layers (usually × then + or −).
- Undo in reverse order — like shoes off before socks.
- For 2x + 3 = 11: first −3, then ÷2.
- PEMDAS builds the expression; solving unwraps it from the outside.
- After the first undo you should have a one-step equation you already know.
Worked examples
Cover the answer. Try the steps on paper, then open them.
Example 1 — Peel + then ×
2x + 3 = 11
- Last thing done to x was +3 (outside).
- Subtract 3 from both sides: 2x = 8
- Divide by 2: x = 4
- Check: 2(4) + 3 = 11 ✓
Answer: x = 4
Check: Unwrap outside first.
Example 2 — See the layers
What two things happened to x in 5x − 2?
- First x was multiplied by 5.
- Then 2 was subtracted.
- So undo: add 2, then divide by 5.
Answer: ×5 then −2
Check: Reverse: +2 then ÷5.
Example 3 — Why not divide first?
If you divide 2x + 3 = 11 by 2 first, you get x + 3/2 = 11/2 — messier.
- The +3 is not inside the ×2 as a single packaged x.
- Subtracting 3 first keeps whole numbers here.
- That is why we peel the add/subtract layer first when it sits outside.
Answer: Subtract first in this shape
Check: 2x + 3 means (2 times x) then plus 3.
Common mistakes
Slip Dividing 2x + 3 by 2 and forgetting the 3.
Fix The 3 is not multiplied by 2 in a way that vanishes. Subtract 3 first.
Outside layer first.
Slip Doing both undos on one side only.
Fix Every undo is a both-sides move.
Balance never sleeps.
Slip Checking only the last line (2x = 8) and not the original.
Fix Check in 2x + 3 = 11.
The original is the truth.
Try on paper first
Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.
1. For 3x + 1 = 13, what do you undo first?
Answer: +1 (subtract 1)
2. 3x + 1 = 13 → after subtracting 1, you have…
Answer: 3x = 12
3. Then x =
Answer: 4
4. Check: 3×4 + 1 =
Answer: 13
Touch practice
8 tap / typeTap 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 practiceReal world
Shoes off before socks.
Connect
Undo a recipe in reverse order.
⭐ Star quiz
9 questionsFinish the touch practice first if you can. Then answer without peeking. Read every “why”.