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## Pre-algebra

### Course: Pre-algebra>Unit 12

Lesson 3: Number of solutions to 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.
• 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.
• 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
• 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.
• Awesome
• When solving an equation of this specific type is the goal only to see if the beginning set of equalities are actually equal to each other? Would a test ever be looking for the value of x in a question like this? i know the problem is in my order of operations in that i keep combining the like terms of the numbers without a variable before the numbers with a variable. I'm led to believe that when solving for x (or the given variable) it would be correct to go in the order opposite of PEMDAS, whereas when given an equation of this type I'm supposed to go in order of like terms with the variable first, am I wrong in thinking this? I think a more valuable thing to ask is if I was given an equation of any type, what about a given equation would lead me to believe that this route would be the one to take? I hope that made sense to someone; I had trouble finding a good way to word this.
• I think Sal was talking way too fast, I didn't really get the term.