Linear expressions · Linear Cup
Linear expressions
These are the first batteries you encounter in Volt Racers. One or two operations, positive whole numbers for x. Once you can do these confidently, the rest of the game builds on top.
One operation, then two
The simplest linear expressions have one operation — a coefficient multiplied by x, then something added or subtracted:
- 3x + 1multiply x by 3, then add 1
- 5x − 4multiply x by 5, then subtract 4
- 2x + 7multiply x by 2, then add 7
Once you're comfortable, two-operation expressions add a second step:
- 4x − 3 + 2multiply, subtract, then add
- 3x + 5 − 1multiply, add, then subtract
The rule stays the same: multiplication first, then left to right.
One operation — 3x + 1 with x = 4
- Replace x with 43 × 4 + 1
- Multiply first12 + 1
- Add13 ✓
Two operations — 4x − 3 with x = 5
- Replace x with 54 × 5 − 3
- Multiply first20 − 3
- Subtract17 ✓
How this appears as a battery
In the game, you see the full equation on the battery — the expression and the result together. Your job is to check: does this hold true for my x value?
x = 5 → Tap it
4 × 5 − 3 = 17 ✓
The equation is true. This battery is correct.
x = 3 → Don't tap it
4 × 3 − 3 = 9, not 17 ✗
The equation is false for x = 3.
Key point
You are not solving for x. You already know x. You are checking whether the equation is true for your x value.
What goes wrong
Mistake 1
Subtracting before multiplying
4x − 3 with x = 5: doing 5 − 3 = 2 first, then 4 × 2 = 8.
4x means 4 times x. That multiplication must happen before the subtraction.
Correct: 4 × 5 = 20 first, then 20 − 3 = 17.
Mistake 2
Forgetting the coefficient
3x + 1 with x = 4: writing 4 + 1 = 5, ignoring the 3.
The 3 is a coefficient — it multiplies x. It cannot be ignored.
Correct: 3 × 4 = 12, then 12 + 1 = 13.
Mistake 3
Checking the wrong x value
Your car shows x = 6 but you evaluate using x = 4 from a previous race.
Your x value changes each race. Always check the number currently shown on your car.
Correct: look at your car before every battery.