How do I "isolate" x in certain equations where other variables are present?

Question

This is a genuine math problem I've stumbled upon several times. One of the most recent equations was this:

3 - 2x = kx - 1

I don't even know if this is possible (if there even is a way to solve this), but of my understanding it is kind of difficult isolating the X here. Though could anyone teach me how? (Im j 15 so if there is a simple explanation I would appreciate that, either way I want to learn)

EDIT: I meant how to isolate "K", I wish I could change the title but I can't. Anyhow thanks for the help :)

Answer 1

This is a linear equation in terms of x, so just move all x terms to one side, and all other terms to the other side.

We have 3-2x = kx-1

Add 1 to both sides : 4-2x = kx

Add kx to both sides: 4 = kx + 2x

Factor out x : 4 = (k+2)x

Now divide : 4/(k+2) = x

Answer 2

Get all the x terms on one side of the equal sign and every else on the other side. Factor out x from - 2x-2k. Divide by (-2-k) on both sides.

Answer 3

it makes absolutely no difference. it's all just the usual operations applied to numbers. x and k are just numbers like any others.

Answer 4

If x was just the number 3, then you would have the equation 3 - 2\*3 = k\*3 - 1. To solve for k, you would add 1 to both sides, then divide both sides by 3.

If x was just the number 2 then you would have the equation 3 - 2\*2 = k\*2 - 1. To solve for k, you would add 1 to both sides, then divide both sides by 2.

The same as if x= 4,-1,pi,... (just not 0, since you can't divide by 0)

The process of how you go about solving it doesn't depend on the particular value of x. That is the essence of algebra. You don't have to know the particular value of x to work with it. You focus on the OPERATIONS.

So to solve 3 - 2\*x = k\*x - 1 for k,

add 1 to both sides of the equation:

4-2\*x = k\*x.

Then divide both sides by x:

(4-2\*x)/x = k