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Brackets and inequalities · Quadratic Grand Prix

Brackets and true or false batteries

Two new things appear in the Quadratic Grand Prix. Brackets — which tell you what to work out first. And batteries that ask true or false instead of giving you a number to match.

Work out the bracket first

When you see brackets, do what is inside them first. Everything else waits.

2(x + 3) − x = 10
Your car: x = 4
  1. Swap x for 4 everywhere
    2(4 + 3) − 4
  2. Work out the bracket first — 4 + 3 = 7
    2 × 7 − 4
  3. Multiply
    14 − 4
  4. Take away
    10 ✓

The battery says 10. Your answer is 10. Tap it.

Brackets first. Always.

Think of them as the game saying: do this bit before anything else.

3(x − 2) + x, with x = 5

3(x − 2) + x = 14
Your car: x = 5
  1. Swap x for 5 everywhere
    3(5 − 2) + 5
  2. Work out the bracket — 5 − 2 = 3
    3 × 3 + 5
  3. Multiply
    9 + 5
  4. Add
    14 ✓

Some batteries are not about matching a number

Most batteries give you a number to match. But some batteries use a > or < sign instead of =.

These batteries are asking a different question: is this true or false for your x?

The four signs you will see:

  • > the left side must be bigger than the right side
  • < the left side must be smaller than the right side
  • ≥ the left side must be bigger than or exactly equal to the right side
  • ≤ the left side must be smaller than or exactly equal to the right side

3x + 1 > 10, with x = 4

3x + 1 > 10
Your car: x = 4
  1. Swap x for 4
    3 × 4 + 1
  2. Multiply first
    12 + 1 = 13
  3. Is 13 bigger than 10?
    Yes. 13 > 10 is true. ✓

This battery is correct. Tap it.

2x − 5 < 4, with x = 4

2x − 5 < 4
Your car: x = 4
  1. Swap x for 4
    2 × 4 − 5
  2. Multiply first
    8 − 5 = 3
  3. Is 3 smaller than 4?
    Yes. 3 < 4 is true. ✓

This battery is correct. Tap it.

What if the answer exactly matches the right side?

x² − 1 ≥ 8
Your car: x = 3
  1. Swap x for 3 — x² means 3 × 3
    3 × 3 − 1
  2. Multiply first
    9 − 1
  3. Take away
    8
  4. Is 8 ≥ 8?
    Yes. 8 equals 8. ≥ includes an exact match. ✓

But if the sign was > instead: is 8 > 8? No. 8 is not bigger than itself. That battery would be wrong. Do not tap it.

Key point

≥ and ≤ include an exact match. > and < do not. The game uses this to trick you. Read the sign carefully.

Three easy mistakes

Mistake 1

Not doing the bracket first

In 2(x + 3) − x with x = 4, some people do 2 × 4 = 8 first. Then 8 + 3 = 11. Then 11 − 4 = 7. Wrong.

The bracket must come first. (4 + 3) = 7. Then 2 × 7 = 14. Then − 4 = 10.

Mistake 2

Mixing up ≥ and >

Seeing 8 ≥ 8 and thinking it is wrong because 8 is not bigger than 8.

≥ means bigger than or equal. Equal counts. It is true.

Mistake 3

Reading > as <

3x + 1 > 10 and 3x + 1 < 10 are completely different. One asks if it is bigger. The other asks if it is smaller.

Slow down and read the sign before you tap.

Try one yourself

Your car: x =

Work out whether the battery is true or false for your x

    Ready for more?

    Next topic

    Powers and negative numbers

    What happens when x is a negative number — and why squaring it gives a positive answer.

    ← Linear expressions
    → Powers and negative numbers Back to the game