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### Course: Pre-algebra>Unit 12

Lesson 3: Number of solutions to equations

# Creating an equation with no solutions

Sal shows how to complete the equation -11x + 4 = __x + __ so that it has no solutions. Created by Sal Khan.

## Want to join the conversation?

• How do I find the value of a constant, such as (k) where there are no solutions? How would I solve it if the equation 4(80 + n) = (3k)n ?
• I think you are saying that you need to find a value of "k" so that the equation will have no solution.
For this to happen...
1) the coefficient of "n" must match on both sides of the equation
2) the constant on each side must be different.

Start by simplifying your equation -- distribute the 4: 320 + 4n = 3kn
The constants on each side are different: 320 on left, and 0 on right. So, one condition is met.
We now know that the coefficient of "n" must = 4. You can find "k" by setting 3k = 4 and solving for "k".

Hope this helps.
• Wait. Equations with no solution cannot apply to something in real life because of the laws of thermodynamics, so if these equations have no real life use why are we learning about them at all. Or do they have a real life use.
• That is actually almost true, but the reason we learn them is to show that there are equations with no answer, but yes there is no real life application since you will never in real life with real problems ever really experience something with no solution.
• Is there any simple trick to find the equation which has no solution without even solving it
• This trick is based on simplifying and as soon as you see the same coefficients of the variable on both sides and any different numbers on the two sides, you know that there are no solutions.
Example: 2(2x+7)= 5x +12 -x
Distribute on left to get 4x +14
Combine like terms on right to get 4x + 12
Since the coefficients of x are both 4, but the constants are different, you know there are no solutions because if you took it to the end, you would get 2=0 which can never be true.
• Am I aloud to just use photomath this is confusing.
• That's if your teacher is okay with it.But if you need help, your teacher can probably help.
• Is there any real world application for making an equation with no solution?
• No, there can't be, because it wouldn't exist. If there is no solution, there can't be an existance.
• I cant wrap my head around this. In the form ax+b=cx+d ... if a!=c then there is apparently only one solution. That means both if ( a!=c AND b=d ) Or ( a!=c AND b!=d) in either case the equation is supposed to have just one result. But for the first option I can rearrange to cancel out b and d so
ax = cx
Now if if I solve for any value of x I get two different values on both sides of the equality, and in my head this would surely indicate that there is no solution.
I can do the same for the second option with the added step of moving b and d around, but still ending up with different values on either side of the equality.
So what have I missed. Is it to do with visualising the equation on a graph or is it some other more obvious fallacy. Im just missing something important about how to think about these equations?
• The thing you are missing is if you get to ax = cx when b=d, you can solve for x.
Subtract either cx or ax from both sides.
ax - cx = 0
"a" and "c" are different values, so when subtracted, they would create some new number (but not zero). Let's call this new number "n" where a - c = n.
Then, ax - cx would = nx.
nx = 0
Divide by n
x = 0/n = 0. (one solution)

Try it. Plus in different values for "a" and "b" and work thru the steps. x = 0 would be solution for when a!=c AND b=d.
• wow i dont get it
• What do you not get?