Solve the given linear equation using multiplication and division properties of equality. − 126 14 = 3 y -\frac{126}{14}=3y

we're asked to solve the given linear equation using multiplication and division properties of equality. The equation we're given here is negative one twenty six over 14 equals three y. So in order to get this y by itself, we need to cancel out that multiplication by our three, which we can do using division. So here, I wanna divide both sides by three. Now because we already have a fraction over here, this looks kind of funny. But remember that if we're taking a fraction and we're dividing it by a fraction, that's really the same thing as just multiplying the fraction by one third. So instead of thinking this of this as division by three, I can think of this instead as multiplication by one third. And we can also think about it this way on this side of our equation just to be clear that we are doing the same exact operation. If I were to take three y and multiply it by one third, those threes are going to cancel out leaving me with just y times one, which is still just y. So on this side, I have y, but over here, I have one third times negative one twenty six over 14. So I can go ahead and multiply my numerators across and my denominators. One times negative 126 will give me a negative 126. Then on the bottom there, three times 14 will give me 42. So this is my answer, but I can actually do some further simplification because 126 or negative 126 is perfectly divisible by 42, and this will actually give me here negative three. So I get that y is equal to negative three as my solution. Now in this case, I can go ahead and plug that negative three back into my original equation and check that I get a true statement. So I have negative one twenty six over 14 and we wanna know is this equal to three times negative three, just plugging that right in. Now negative one twenty six over 14, I'm gonna keep that the same for now and just focus on this multiplication. Three times negative three gives me negative nine. Now looking at this, you may be thinking, okay, that's not a true statement. Those are definitely not the same thing. But one twenty six is actually divisible by 14 And if I perform that division, I will get here negative nine. So negative nine equals negative nine. That's definitely a true statement and this is a correct answer. Now, in fact, because one twenty six is divisible by 14, I could have done that division at the very beginning and instead been solving the equation that negative nine is equal to three y, which looks quite a bit simpler. As you continue practicing working through more and more problems, you'll develop a better sense for recognizing those things earlier on. For now, let's continue practicing. I'll see you in the next one.

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Solve the given linear equation using multiplication and division properties of equality.−12614=3y-\(\frac{126}{14}\)=3y

다음 시청

Solve the given linear equation using multiplication and division properties of equality.
$- \frac{126}{14} = 3 y$