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# Number of solutions to equations: 8(3x+10)=28x-14-4x

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.

Video transcript

Solve for x: we 8 time the quantity 3x + 10 is equal to 28x - 14 - 4x Like every equation we've done so far, we just want to isolate all the x's on one side of this equation. But before we do that, we can actually simplify each of these sides. The left hand side: we can multiply the quantity 3x + 10 times 8 so we're essentially just distributing the 8 (distributive property right here) So this is the same thing as 8 times 3x which is 24x plus 8 times 10 which is 80 is equal to and over here we have 28x - 14 - 4x so we can combine the 28x and the -4x 28x - 4x that is 24x and then you have the -14 right over here. Now the next thing we can do and it's already looking a little bit suspiscious but just to confirm that it's as suspicious as it looks, let's try to subtract 24x from both sides of this equation. And if we do that, we see that we actually remove the x's from both sides of the equation because we have 24x there and we have a 24x there. You might say, "Hey, let's put all the x's on the left hand side so let's get rid of this 24x" so you subtract 24x right over there but have to do it to the left hand side as well. And then we're left with: on the left hand side these guys cancel out you're left with just 80 is equal to is equal to – these guys cancel out as well – is equal to -14 Now this looks very bizarre. So we're making a statement that 80 is equal to -14 which we know is not true. This does not happen 80 is never equal to -14, they're just inherently inequal. So this equation right here actually has no solution. This has no solution. There is no x value that will make 80 equal to -14