Question Video: Solving Rational Equations in One Variable

Solve the equation 1/2 = (2/(3𝑥)) − 1.


Video Transcript

Solve the equation a half equals two over three 𝑥 minus one.

So in order to solve this equation, what we are trying to do is actually find 𝑥. As you can see we’ve actually got fractions involved. But we can actually deal with those in a second. So the first thing we’re gonna do is actually add one to each side of the equation. And when we do that, we’re gonna get three over two is equal to two over three 𝑥.

And the reason we got that is because if we have a look here we a half add one, whereas a half add is equivalent of two halves, which is gonna be three over two or three-halves.

Okay, great, so now what’s the next stage? Well, the next stage is to actually multiply by three 𝑥 because actually we want to make sure that our 𝑥 is not on the denominator cause we’re trying to find 𝑥. So we’ve got three multiplied by three 𝑥 over two equals two. So therefore, if we simplify this, we’re gonna get nine 𝑥 over two equals two.

So now, we’re gonna multiply each side of the equation by two. And therefore, we’re gonna get nine 𝑥 equals four. And that’s because if you have nine 𝑥 over two multiplied by two, this gives us nine 𝑥. Then two multiplied by two gives us four.

And the final stage is to actually divide each side of the equation by nine. And when we do that, we get 𝑥 is equal to four over nine or four-ninths.

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