Absolute value is the distance a number is from 0 on a number line.

📌 The most important rule:
✅ Absolute value is always non-negative (never negative)

We write absolute value using bars:

∣x∣

⭐ Key Idea

Absolute value tells you how far a number is from 0, not what direction.

So:

• ∣5∣ = 5

• ∣−5∣ = 5

Both are 5 units away from 0, just on opposite sides of the number line.

🔢 Absolute Value on a Number Line

Think of the number line:

… -3, -2, -1, 0, 1, 2, 3 …

• −3 is 3 steps from 0 → ∣−3∣= 3

• 2 is 2 steps from 0 → ∣2∣ = 2

🧠 Absolute Value Rule (Simple)

For any number x:

∣x∣ = {x if x ≥ 0

        {−x if x < 0​

Meaning:

• If the number is positive or 0, keep it the same.

• If the number is negative, make it positive.

Example:

• ∣−12∣ = 12 

• ∣0∣ = 0

🔥 Why Absolute Value Matters (Real Life)

Absolute value is used whenever you care about the size of a difference but not the direction.

Examples:
✅ Temperature change

• If it goes from 3° to -2°, the change is:

 ∣3 − (−2)∣ = ∣5∣ = 5

✅ Distance

• Distance between -7 and 4 is:

∣−7 − 4∣ = ∣−11∣ = 11

✅ Error / how far off you are

• If you predicted 50 but the answer is 46:

∣50 − 46∣ = 4