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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 + 1
    multiply x by 3, then add 1
  • 4x − 3
    multiply x by 4, then take away 3
  • 5x + 7
    multiply 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

3x + 1 = 13
Your car: x = 4
  1. Swap x for 4
    3 × 4 + 1
  2. Multiply first
    12 + 1
  3. Add
    13 ✓

The battery says 13. Your answer is 13. Tap it.

4x − 3 = 17, with x = 5

4x − 3 = 17
Your car: x = 5
  1. Swap x for 5
    4 × 5 − 3
  2. Multiply first
    20 − 3
  3. Take away
    17 ✓

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

2x + 5
  1. Swap x for 6
    2 × 6 + 5
  2. Multiply first
    12 + 5
  3. Add
    17
5x − 4
  1. Swap x for 6
    5 × 6 − 4
  2. Multiply first
    30 − 4
  3. Take away
    26
10 − x
  1. Swap x for 6
    10 − 6
  2. Take away
    4

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.

Try one yourself

Your car: x =

Work out the answer and type it in

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