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### Course: Algebra (all content)>Unit 2

Lesson 9: Analyzing the number of solutions to linear equations

# Worked example: number of solutions to equations

Sal attempts to solve 8(3x + 10) = 28x - 14 - 4x only to find that the equation has no solution. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• did i do something wrong i only got the number left

Solve for X
8(3x + 10) = 28x – 14 – 4x
Multiplied the numbers in the brackets
24x + 80 = 28x – 14 – 4x
Compressed the 2 ‘x’ numbers left side
24x + 80 = 24x – 14
got rid of the 14 on the right by add 14 to both sides and Took away the 24 by x on both sides
94
• 24𝑥 − 24𝑥 + 94 = 24𝑥 − 24𝑥
0 + 94 = 0
94 = 0

This is of course a false statement and means that the equation doesn't have a solution.
No matter what value of 𝑥 we put into the equation we will never get equality.
• It kind of makes sense, kind of. But we'll all get it someday!
• If you are solving a problem and you come to one of these special cases, can you just write null set? The symbol is like a 0 with a line crossing diagonally through it. On a test just drawing the symbol might be easier and less time consuming, hence my question.
• I'm not exactly sure if you can use that, some teachers may agree other may not. To be on the safer side I recommend that you say 'No Solution' as an answer. Since we couldn't find what 'x' was exactly there wasn't a solution to the answer.

I hope this helped.
• 3-3=0
2-2=0
Concludion: 2=3
• You have a false conclusion.
The inverse property of addition tells us that if you subtract a number from itself, it will always = 0.

It does not tell you that if you apply the property multiple times that the 2 numbers you used will equal each other.
2 will never equal 3.
• why are functions so hard for me even though that we have studied them for weeks
• Not sure. Have you considered asking a teacher to try to explain?
• is this actually a equation at all? I'm not sure
• then the equation has infinite solutions
• What can help me with the quiz, Re watching the video or redoing it?
• I would rewatch the video and watch any other videos on the topic you need help with.
• How can you tell that the question has no solution and not that something was done wrong in the problem (such as multiplying something wrong)?
• Hey Star Brightscales!
If you take your x factor and put it back into the original equation, you will see that the answers are not the same. Basically, just check your work and you will see that it's not right.
Hope this helps!
-Abbie