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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:
$\begin{array}{rl}& 4x+3x\\ \\ =& \left(4+3\right)x\\ \\ =& 7x\end{array}$

## More examples

An example with more than two terms:
$\begin{array}{rl}& 2r+1+\left(-4r\right)+7\\ \\ =& 2r-4r+1+7\\ \\ =& \left(2-4\right)r+1+7\\ \\ =& -2r+8\end{array}$
An example with more than one variable:
$\begin{array}{rl}& 3x+2y+4x+7-y\\ \\ =& 3x+4x+2y-y+7\\ \\ =& \left(3+4\right)x+\left(2-1\right)y+7\\ \\ =& 7x+y+7\end{array}$

Problem 1
Combine the like terms to make a simpler expression.
$-3n-7+\left(-6n\right)+1$

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

## Want to join the conversation?

• Why am i not getting this :(
• 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.
• uhhhhhhgg why have i failed like every single timeeeeeeeee
• what is 9t−3t+4
• That would be 6t+4 because 9t-3t=6t and 4 is just left alone so it equals 6t+4.

• the only thing i'm really confused about is how to do the fractions part
• 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
• 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?
• This is driving me crazy!
• How would I combine like terms if there is a variable as the numerator and not as the coefficient?

Like: w/60 + w/5
• 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.
• 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