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## College Algebra

### Unit 1: Lesson 1

Solving equations with one unknown

# 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
• 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
• 24x and -24x on the left hand side of the equation
• What if the equation simplifies to something like 5x equals 3x? Would zero count as a solution to this equation, making the number of solutions that this equation has 1?
• Wait, stupid question, why can't we subtract the 80 first, and then divide 24x by 24?
• You could subtract 80 first. But, dividing by 24 doesn't help you solve for X. You need to get all the X's on the same side. So, at some point, you need to subtract the X's. If you divide, you are just making extra work by introducing a step that is not needed.
Hope this helps.