Adding and Subtracting Linear Expressions
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Adding Linear Expressions: Collecting Like Terms
Imagine you're organizing your backpack before school. You wouldn't mix pencils with erasers — you'd group like items together. Linear expressions work the same way: you can only combine terms that are "alike."
A linear expression is like a mathematical recipe that mixes variables (usually x) with regular numbers. When we add two linear expressions, we're essentially combining two recipes — but we can only add ingredients of the same type.
The "Like Terms" Rule
Think of terms as different types of objects:
- x-terms:Like apples (3x, 7x, -2x)
- constant terms:Like oranges (5, -8, 12)
You can add apples to apples and oranges to oranges, but you can't simplify apples plus oranges!
Real Example: School Supply Budget
Sarah's expression: (4x + 7) — She needs 4 notebooks at $x each, plus $7 for pens
Jake's expression: (2x - 3) — He needs 2 notebooks at $x each, minus a $3 discount
Combined budget: (4x + 7) + (2x - 3)
Step 1: Remove parentheses → 4x + 7 + 2x - 3
Step 2: Group like terms → (4x + 2x) + (7 - 3)
Step 3: Combine → 6x + 4
💡 The Invisible 1
Here's something that trips up many students: when you see just x, there's actually an invisible coefficient of 1 in front of it.
x + 3x is really 1x + 3x = 4x
Think of it like saying "1 apple + 3 apples = 4 apples" — we just don't usually say the "1" out loud!
Watch Out for Signs!
When adding expressions, pay special attention to negative signs. Remember that subtracting a positive is the same as adding a negative: (5x + 2) + (-3x + 4) = 5x + 2 - 3x + 4 = 2x + 6
🔑 Key Takeaway
Just like organizing your backpack, adding linear expressions is all about grouping like items together. Variables stay with variables, numbers stay with numbers, and the result is one clean, simplified expression that represents the sum of both original "recipes."
Sample questions
Skills in this topic
- Add two linear expressions
- Subtract two linear expressions
- Add and subtract linear expressions with fractional coefficients
- Write an expression for the perimeter of a geometric figure
- Find the missing side length of a figure when given the perimeter expression
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