Question

Solve for x 2/3(x-2)=4x

Answer 1

So, this is the equation which we want to solve for x:

\[\frac{ 2 }{ 3 } (x -2) = 4x\]

Let's start first by multiplying out the bracket on the left-hand side:
\[\frac{ 2 }{ 3 }x + \frac{ 2 }{ 3 }(-2) = 4x\]
\[\frac{ 2 }{ 3 }x -\frac{ 4 }{ 3 } = 4x\]

We can bring the '(2/3)x' over to the right-hand side of the equation. In doing so, we must change the sign on it. This means we get:
\[-\frac{ 4 }{ 3 } = 4x -\frac{ 2 }{ 3 }x\]

As the two terms on the right-hand side are both in terms of 'x', we can subtract them from one another to get:
\[-\frac{ 4 }{ 3 } = \frac{ 10 }{ 3 }x\]

As you can see, we have a fraction on both sides of the equation which means that we are essentially dividing both sides (the -4 on the left and the 10x on the right) by 3. As we are doing the same thing to both, we can cancel the two 3s to leave us with:
\[-4 = 10x\]

We need to get x on its own. In order to do this, we can divide both sides of the equation by 10. This will leave us with:
\[\frac{ -4 }{ 10 } = \frac{ 10x }{ 10 }\]

On the right-hand side, the two 10s on the top and bottom of the fraction will cancel each other out, to leave us with the answer, and the equation solved for 'x'! :)