Solve the given linear equation. 2 3 x = 10 \frac23x=10

we're asked to solve the given linear equation. The equation we're given here is two thirds X equals 10. Now, because I'm dealing with a fraction coefficient, that means that I'm going to want to multiply by its reciprocal in order to cancel that fraction out so that I can get X all by itself. So here I have the fraction two thirds. If I flip that fraction, that gives me three halves. So three halves times two thirds X, that will end up canceling. But if I'm multiplying by three halves on that side of my equation, I need to multiply by three halves on the other side as well. So I have 10 times three halves over here. Now, like we said before, these are going to cancel out, just leaving me with X. So I have that x is equal to 10 times three halves. Now we can think of this 10 as being 10 over one and just multiply across. Multiplying my numerators 10 times three gives me 30. And then on the bottom there, one times two just gives me two. Now I can do some further simplification because 30 is divisible by two. That gives me 15. So I get that X is equal to 15 and this is my final answer. And we can of course check our answer by plugging that 15 back into our original equation and checking that it gives us a true statement. So that's two thirds times 15. We want to know, is this going to give us a true statement? Is this equal to 10? Now, looking at this multiplication here, I can think of this 15 as being 15 over one, multiply my numerators across and my denominators across. Two times 15 will give me 30. Then on the bottom there, three times one just gives me three. So 30 over three, is this equal to 10? Well, 30 divided by three is 10, so I get my answer here that 10 equals 10. This is definitely a true statement, so I know that I solved my equation correctly, and x is equal to 15.