Given the equation y = 1 2 x − 4 3 y=\frac12x-\frac43 , what is the missing variable shown below? (__, 20 3 \frac{20}{3} 3 20 )

this problem, we are given the equation y equals one half x minus four thirds, and we want to find the missing variable shown below. Now looking at my ordered pair here, it's going to be in the form x y. I can see that my y is given, so it's the x that I don't know. So going to our equation, we need to figure out what x is. So what I'm going to do is rewrite this. Now y, I can see here is going to be 20 over three. And that's going to be equal to one half x minus four thirds. And I just need to solve for x. Now to solve this, well, I'm gonna start by adding four thirds to both sides of the equal sign. Doing that is going to cancel the four thirds on the right side, leaving me with just one half x. Now, one half x is going to equal 20 over three plus four over three, which I can just add the numerator since we have the same denominator of three. That's gonna give me 24 over three. Now, can we reduce this 24 over three? Well, something that I know is that 24 is the same thing as three times eight. Then in the denominator, we have three, so I can cancel those threes. So it's gonna give me that one half x is equal to eight. Now what I need to do from here is multiply both sides of the equal sign by two, and that will get the two to cancel in the numerator and denominator of one half, leaving me with just one x, or we could just write that as x. That's going to equal eight times two, which is 16. So x is equal to 16 and because we figured out x is 16 that means 16 is the missing number in this ordered pair which is the solution to this problem. Hope you found this helpful.

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Multiple Choice

Given the equation $y = \frac{1}{2} x - \frac{4}{3}$ , what is the missing variable shown below?
(__, $\frac{20}{3}$ )

$8$

$12$

$24$

$16$

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