Practice Linear Equations
A linear equation has the form ax + b = c.
- Subtract b from both sides: ax = c − b
- Divide both sides by a: x = (c − b) / a
Example: 2x + 3 = 11 → 2x = 8 → x = 4
🍎 In the fruit basket:
The basket has 3 apples and 5 more apples.
Simplify the expression: \(3a + 5a\)
💡 Explanation — What are like terms?
🍎 Using apples as an example:
3 apples + 5 apples = 8 apples
📐 In algebra:
\(3a + 5a\)
The two terms share the same variable (a) — they are like terms.
🔢 How do we simplify?
Add the coefficients: \(3 + 5 = 8\)
The variable stays: \(a\)
Answer: \(8a\)
✨ Golden rule: Like terms share exactly the same variable!
You can combine them by adding or subtracting their coefficients.
🍌🍊 Mixed basket:
The basket has 4 bananas and 3 oranges.
Can this expression be simplified? \(4b + 3o\)?
💡 Explanation — Why cannot this be simplified?
🍌🍊 Using fruit as an example:
4 bananas + 3 oranges = 4 bananas and 3 oranges.
You cannot say "7 somethings" — they are not the same thing!
📐 In algebra:
\(4b + 3o\)
b and o are different variables — these are unlike terms.
🚫 Important rule:
You can only combine terms with exactly the same variable!
✅ Like terms: \(3x + 5x\) ← same variable
❌ Unlike terms: \(3x + 5y\) ← different variables
💭 Think: you cannot add apples and bananas into one number!
🥕 Carrots in the garden:
We picked 7 carrots and ate 3 carrots.
Simplify the expression: \(7c - 3c\)
💡 Explanation — Subtracting like terms
🥕 Using carrots as an example:
7 carrots − 3 carrots = 4 carrots
📐 In algebra:
\(7c - 3c\)
Both terms share the same variable (c) — they are like terms.
🔢 How do we subtract like terms?
Subtract the coefficients: \(7 - 3 = 4\)
The variable stays: \(c\)
Answer: \(4c\)
✨ Rule for subtraction:
Just like addition — subtract the coefficients!
\(7c - 3c = (7-3)c = 4c\)
💭 Remember: always check that the variable is identical before simplifying!
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