Chapter 11: Combining Like Terms

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

11.1 What are "Like Terms"?

In Algebra, a "term" is a number, a variable, or a product of both. To be Like Terms, two terms must have the exact same variables with the exact same exponents. The only thing that can be different is the coefficient (the number in front).

Like Terms: 3x and 10x (Both are in the x family).
Unlike Terms: 3x and 3x² (They look similar, but the exponent makes them different families).

11.2 The "Fruit Basket" Analogy

Imagine a basket containing 3 apples, 2 oranges, and 5 more apples. You wouldn't say you have "3a + 2o + 5a." You would group the apples together to say you have 8 apples and 2 oranges.

Example: Simplify 4x + 7 + 2x - 3

Identify the x-family: 4x + 2x = 6x
Identify the number-family: 7 - 3 = 4
Result: 6x + 4

11.3 Watch the Signs!

The sign (+ or -) belongs to the term that follows it. This is where most errors occur. If you see 5x - 8x, think of it as "positive 5 and negative 8."

Problem: Simplify 10y - 4 + 2y + 9

Y-Terms: 10y + 2y = 12y

Numbers: -4 + 9 = 5

Final Answer: 12y + 5

11.4 Putting it Together

Now we can combine Chapter 10 (Distributing) with Chapter 11 (Combining). This is the foundation of solving equations.

Simplify: 2(x + 3) + 4x

First, Distribute: 2x + 6 + 4x
Then, Combine: 6x + 6

Chapter 11 Review

Simplify the following expressions:

8a + 2a + 5
12x - 3x + 4y - y
5 + 2x - 3 + 4x
3(x + 2) - 1

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Doctor's Recommendation: Vertical Alignment

Chapter 11 is where math starts to get long. If your work drifts across the page, you'll lose your variables. A Quad-Ruled Notebook provides a grid that forces you to keep like terms vertically aligned, turning a messy problem into a clean, logical flow.

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