Linear expressions · Linear Cup
Batteries with + and −
These are the first batteries you see in the game. A number multiplied by x, then something added or taken away. Once you can do these, everything else builds on top.
The pattern is always the same
Every battery at this level follows the same pattern:
something × x, then + or − a number
- 3x + 1multiply x by 3, then add 1
- 4x − 3multiply x by 4, then take away 3
- 5x + 7multiply x by 5, then add 7
The number in front of x tells you what to multiply by. The number at the end tells you what to add or take away.
3x + 1 = 13, with x = 4
- Swap x for 43 × 4 + 1
- Multiply first12 + 1
- Add13 ✓
The battery says 13. Your answer is 13. Tap it.
4x − 3 = 17, with x = 5
- Swap x for 54 × 5 − 3
- Multiply first20 − 3
- Take away17 ✓
The battery says 17. Your answer is 17. Tap it.
You are checking, not solving
The battery shows you the full thing — the sum and the answer. Your job is just to check whether it is true for your x.
x = 5 → Tap it
4 × 5 − 3 = 17 ✓
True for x = 5. This battery is yours.
x = 3 → Don't tap it
4 × 3 − 3 = 9, not 17 ✗
Not true for x = 3. Leave it.
Key point
You already know x. You are not finding x. You are just checking if the battery is right for your x.
Have a go at these — all with x = 6
- Swap x for 62 × 6 + 5
- Multiply first12 + 5
- Add17
- Swap x for 65 × 6 − 4
- Multiply first30 − 4
- Take away26
- Swap x for 610 − 6
- Take away4
This one has no multiply step. Just swap and take away.
Two easy mistakes to avoid
Mistake 1
Taking away before multiplying
In 4x − 3 with x = 5, some people do 5 − 3 = 2 first. Then 4 × 2 = 8. Wrong answer.
Multiply first. 4 × 5 = 20. Then take away 3. Answer: 17.
Mistake 2
Forgetting the number in front of x
In 3x + 1 with x = 4, some people just do 4 + 1 = 5. They forgot to multiply by 3.
The 3 is always there. Always multiply by it first. 3 × 4 = 12, then 12 + 1 = 13.