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### Course: Algebra (all content) > Unit 1

Lesson 8: Combining like terms- Intro to combining like terms
- Combining like terms with negative coefficients & distribution
- Combining like terms with distribution
- Combining like terms with distribution
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Combining like terms with rational coefficients
- Combining like terms review

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# Combining like terms review

A common technique for simplifying algebraic expressions. When combining like terms, such as 2x and 3x, we add their coefficients. For example, 2x + 3x = (2+3)x = 5x.

## What is combining like terms?

We call terms "like terms" if they have the same variable part. For example, $4x$ and $3x$ are like terms, but $4x$ and $3w$ are not like terms.

The cool thing about like terms is that we can combine them into a single term by adding their coefficients. For example:

*Want to learn more about combining like terms? Check out this video.*

## More examples

An example with more than two terms:

An example with more than one variable:

## Check your understanding

*Want more practice like this? Check out this exercise and this other exercise.*

## Want to join the conversation?

- Why am i not getting this :((17 votes)
- Suppose the temperature is a freezing -6 degrees.

It gets even colder than that by 16 degrees. (subtracting)

Now it's an even more freezing -22 degrees.(11 votes)

- uhhhhhhgg why have i failed like every single timeeeeeeeee(14 votes)
- what is 9t−3t+4(6 votes)
- That would be 6t+4 because 9t-3t=6t and 4 is just left alone so it equals 6t+4.

(I hope this can help you) :)(4 votes)

- the only thing i'm really confused about is how to do the fractions part(6 votes)
- You just have to know how to add, subtract, multiply and divide fractions and the simplifying algebraic expressions with fractions in them will become fairly easy :D(4 votes)

- I just don't understand the negatives! In one problem I must subtract and in an other one I must add... can some one help me?(2 votes)
- You need to understand how to add / subtract signed numbers. It sounds like you are still confused with that concept. I would recommend you redo the lessons for adding and subtracting signed numbers. There are 3 sections starting at this link: https://www.khanacademy.org/math/pre-algebra/pre-algebra-negative-numbers#pre-algebra-add-negatives-intros

Hope this helps.(10 votes)

- This is driving me crazy!(4 votes)
- How would I combine like terms if there is a variable as the numerator and not as the coefficient?
*Like:***w/60**+**w/5**(2 votes)- You have 2 like terms and your terms are fractions. Convert them to have a common denominator, then add the numerators. There is a video with a similar problem at: https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-manipulating-expressions/v/simplifying-expressions-involving-rational-numbers

Note: w/60 is the same as (1/60)w, they have just been multiplied together (numerator to numerator and denominator to denominator).

Hope this helps.(5 votes)

- Can someone help me with the problem 3x - 12 = 2x -4 + 3x + 6

I'm so confused on how to solve it, because I got 2 answers: one was -14/8 and one was 14/8. Which one is the right one?(1 vote)- Neither is correct. I confirmed this by substituting each value in the equation to see if the 2 sides are equal. In both cases, the 2 sides are unequal.

Here's correct solution:

1) Combine like terms on right side: 3x-12 = 5x+2

2) Subtract 3x from both sides: -12 = 2x + 2

3) Subtract 2 from both sides: -14 = 2x

4) Divide both sides by 2: -7 = x

Checking solution:

3(-7) - 12 = 2(-7) -4 + 3(-7) + 6

-21 - 12 = -14 -4 + -21 + 6

-33 = -18 + -15

-33 = -33

So x=-7 is the correct answer

Hope this helps.(6 votes)

- how can you subtract negative integers(1 vote)
- If you have -2 - (-4) the subtraction sign and the negative sign for the second number cancel out so it becomes -2 + 4.

If you have -2 - 4 you simply add the 4 to 2 and put the negative sign in front(4 votes)

- how do I combine like terms in a problem with fractions?(2 votes)
- Then you follow the rules for adding/subtraction fractions:

-- Find an LCD

-- Convert the fractions to the LCD

-- Add/subtract the numerators.

Hope this helps.(2 votes)