Question

Solve the following equation:

\[\frac{ 1 }{ 3 }(2x - 5) -2 = \frac{ 1 }{ 2 }(x - 2)\]

Answer 1

Do you know how to isolate variables?

Answer 2

Depends, what do you mean?

Answer 3

You need to have it so \(x\) is on one side of the equation, and there is just a number, the value of \(x\), on the other side.

Answer 4

Oh, well then yes, I do.

Answer 5

You have to do things like multiplying both sides by numbers, addition, subtraction, etc.

Answer 6

If you want to get rid of the fractions in this case, you'd multiply both sides by 2, and then by 3.

Answer 7

Would it look like: \[\frac{ 2 }{ 1 } \times \frac{ 1 }{ 3 }( 2x - 5) - 2 = \frac{ 2 }{ 1 } \times \frac{ 1 }{ 2 } (x - 2) ?\]

Answer 8

The 2 on the other half of the equation is supposed to be a 3. But yeah, I get it now. Without the fractions it's waaay easier. Thanks for the help.

Answer 9

The multiplication distributes over the minus and onto the 2 as well.

Answer 10

It would look like: \[\frac{ 2 }{ 1 } \times \left[\frac{ 1 }{ 3 }( 2x - 5) - 2 \right] = \frac{ 2 }{ 1 } \times \left[ \frac{ 1 }{ 2 } (x - 2) \right] \]

Answer 11

Ohhhh. Okay, okay. I see. So the same bottom denominator just goes away right?

Answer 12

yeah

Answer 13

Thanks for all the help, I really appreciate it!