 This video will be translating English sentences into an equation that we can then solve. So the first thing we need to do is to be able to figure out what our unknown is and what it represents so that we can then translate into the equation, solve it, and then write a sentence at the final step. So we have this problem. The difference of a number in 10 is negative 55 and says find the number. Basically when you look at what it asks you to find you'll be able to figure out what your variable is supposed to be. So I'm going to let the variable be in and it's going to represent the number. So now we're ready to translate. So when you see the difference remember that's subtract and a number that's our variable that's the in and 10 is translates to equal negative 55. So let's do that. We have a difference of the number in 10 is negative 55. So now we're ready to solve. Our subtracting 10 from this end so to get it to the other side we have to do the opposite or add 10 to both sides. So n is going to be equal to negative 45. And if we check that just to make sure we found the right number negative 45 would be our in minus 10 is equal to negative 55 and we add the opposite here. We have negative 45 plus a negative 10 which is a negative 55 and it's still equal to our negative 55. So our number really is negative 45 and that's what we write as our sentence. The number is negative 45. Three times the number equals twice the sum of the number in 12. Alright we have a number it says find the number so that again is going to be our variable. The sum is going to let it be x just because you can use any variable you want to. So I'm going to change it up. So this is our number. So we have three times the number equal that's obvious what you're going to translate that one to twice the sum so two times the sum of the number in 12. This is kind of tricky but let's just take it one step at a time three times the number so that's three n equal then twice means two times but two times what? Two times the sum. So that means we need to have a parenthesis that we can contain our sum and the sum is going to be the number n12. So now we're ready to solve. We need to copy down three n on this side but we need to distribute on the right hand side. So two times n will be two n and two times 12 will be plus 24 and when I'm solving I'm going to subtract the two n so that I can get the 24 by itself and collect all the n's on the other side and three n is larger so I'm going to subtract two n that leaves me with n equal 24 okay so let's check that just to double check. So three times 24 I'm going to run out of space here so I'll do this side and then I'll do the other side 72 and on the other side we have two times 24 that's equal to two times 36 which is equal to 72 and both these numbers are the same so we know that the number is 24. We answered the question they asked us. One last one six less than five times the number is more than four times the number so here we are again we need to choose a variable and let's just go back to n for number and it is the number so six less than remember six less than means that my order is going to switch and then five times a number and we called that n is translates to equal two more that means more than means plus four times so four times and then the number so we switched the order so I do the five times first so five times a number less than my six so it's six less than five times my number is two more than four times the number so two plus four n okay now we're ready to solve we've got n's on both sides we've got constants on both sides let's move the n so that we can keep it positive so four n is smaller than five n so I'm going to subtract four n from both sides and so on this side I have n but I still have minus six equal to two now I want to get the six to the right hand side so it's being subtracted so to take it to the other side I have to do the opposite and add six and that tells us that n is equal to eight so if I come back over here and double check it I have five times n which is eight minus six should be equal to two plus four times n which is eight five times eight is forty minus six and forty minus six would be thirty four equal to and on this side we have two plus four times eight is thirty two and two plus thirty two is thirty four so we know that the number is eight