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.

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) :)

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?

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.

How would I combine like terms if there is a variable as the numerator and not as the coefficient? _Like:_ *w/60* + *w/5*

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.

how do I combine like terms in a problem with fractions?

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.

how can you subtract negative integers

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

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?

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.

Main content

Algebra (all content)

Course: Algebra (all content) > Unit 1

Lesson 8: Combining like terms

Combining like terms review

Google Classroom

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}

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

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}

Check your understanding

Problem 1

Current

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.

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danielle_moreland
Posted 7 years ago. Direct link to danielle_moreland's post “Why am i not getting thi...”
Why am i not getting this :(
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(18 votes)
Answer
- p.bruggemans
  Posted 7 years ago. Direct link to p.bruggemans's post “Suppose the temperature i...”
  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.
  Comment on p.bruggemans's post “Suppose the temperature i...”
  (11 votes)
Holly Wenk
Posted 4 years ago. Direct link to Holly Wenk's post “uhhhhhhgg why have i fail...”
uhhhhhhgg why have i failed like every single timeeeeeeeee
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(13 votes)
Answer
t.stanle2
Posted 4 years ago. Direct link to t.stanle2's post “what is 9t−3t+4”
what is 9t−3t+4
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(6 votes)
Answer
- James Gallagher
  Posted 2 years ago. Direct link to James Gallagher's post “That would be 6t+4 becaus...”
  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) :)
  Comment on James Gallagher's post “That would be 6t+4 becaus...”
  (4 votes)
Brooklyn Scott
Posted 7 years ago. Direct link to Brooklyn Scott's post “the only thing i'm really...”
the only thing i'm really confused about is how to do the fractions part
Button navigates to signup pageComment on Brooklyn Scott's post “the only thing i'm really...”
(5 votes)
Answer
- Avada Spike
  Posted 7 years ago. Direct link to Avada Spike's post “You just have to know how...”
  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
  Button navigates to signup page
  (5 votes)
Rexmin
Posted 6 years ago. Direct link to Rexmin's post “I just don't understand t...”
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?
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(2 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “You need to understand ho...”
  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.
  Button navigates to signup page
  (10 votes)
ashleyd
Posted 2 years ago. Direct link to ashleyd's post “This is driving me crazy!”
This is driving me crazy!
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(4 votes)
Answer
Aarna Desai
Posted 4 months ago. Direct link to Aarna Desai's post “How would I combine like ...”
How would I combine like terms if there is a variable as the numerator and not as the coefficient?

Like: w/60 + w/5
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(2 votes)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “You have 2 like terms and...”
  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.
  Comment on Kim Seidel's post “You have 2 like terms and...”
  (4 votes)
meganbarahona91
Posted 5 years ago. Direct link to meganbarahona91's post “how can you subtract nega...”
how can you subtract negative integers
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(1 vote)
Answer
- kashyap14
  Posted 5 years ago. Direct link to kashyap14's post “If you have -2 - (-4) the...”
  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
  Button navigates to signup page
  (4 votes)
Zarin Moon
Posted 3 years ago. Direct link to Zarin Moon's post “Can someone help me with ...”
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?
Button navigates to signup pageComment on Zarin Moon's post “Can someone help me with ...”
(1 vote)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “Neither is correct. I co...”
  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.
  Button navigates to signup page
  (4 votes)
shaws250
Posted 3 years ago. Direct link to shaws250's post “how do I combine like ter...”
how do I combine like terms in a problem with fractions?
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(2 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “Then you follow the rules...”
  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.
  Button navigates to signup page
  (2 votes)