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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, 4, x and 3, x are like terms, but 4, x and 3, w 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{aligned} &4x+3x\\\\ =&(4+3)x\\\\ =&7x \end{aligned}

More examples

An example with more than two terms:
\begin{aligned} &2\blueD{r} + 1 + (-4\blueD{r}) + 7\\\\ =& 2\blueD r - 4\blueD{r} + 1 + 7 \\\\ =& (2 - 4)\blueD{r} + 1 + 7 \\\\ =& -2\blueD{r} + 8 \end{aligned}
An example with more than one variable:
\begin{aligned} &3\blueD{x} + 2\goldD{y} + 4\blueD{x} + 7 -\goldD{y}\\\\ =&3\blueD{x} + 4\blueD{x} + 2\goldD{y} -\goldD{y}+7\\\\ =& (3+4)\blueD{x} + (2-1)\goldD{y} + 7 \\\\ =& 7\blueD{x} + \goldD y + 7 \end{aligned}

Problem 1
Combine the like terms to make a simpler expression.
minus, 3, n, minus, 7, plus, left parenthesis, minus, 6, n, right parenthesis, plus, 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?
• 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
• how do I combine like terms in a problem with fractions?
-- Find an LCD
-- Convert the fractions to the LCD

Hope this helps.
• 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.