If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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.
• 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.
• 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
• Guys, I think Sal attempts to solve 8(3x + 10) = 28x - 14 - 4x only to find that the equation has no solution.
• 3-3=0
2-2=0
Concludion: 2=3
(1 vote)
• 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.
• I think Sal was talking way too fast, I didn't really get the term.
• If there is no solution then does that mean that there could be other answers ?
• HI!

I just want to ask, At what do Sal meant by these guys