How would you solve a problem like "x = 6x-210?"?

Question

I'm not necessarily looking for the exact answer, but rather, steps to find the answer. I know that substituting-in is one way, but how would I solve this algebraically?

Answer 1

x + 210 = 6x
210 = 5x
x = 210 / 5
x = 42

Answer 2

Get the x terms by themselves. The simplest way to do this is to subtract 6x from both sides. This gives you -5x = -210. Now get rid of the -5 by dividing both sides by -5. This gives you x = 42.

Notice I kept saying "do this on both sides". In general, you make use of the fact that if something is equal to something else, then you can safely do the same operation on either side of the equals sign. The goal is to do this in such a way that you finally wind up with the equation as "x = some number".

You don't want to get into the practice of plugging in numbers and trying to check to find something that works. That's just not going to be reliable when you get to equations that are even just slightly more complicated.

Answer 3

Well, you can combine "like terms" together. To do this, add, subtract, multiply or divide both sides of the equation by the same value to keep the equality:

x - 6x = 6x - 210 - 6x { Combine like terms ("x" factors) }

-5x = -210 { Multiply both sides by -1 }

5x = 210 { Divide both sides by 5 }

x = 42

Answer 4

If x =6x-210 then 5x=210, thus x=42

Answer 5

x=6x-210
5x=210, collected all terms containing x on the right sideand the rest on the left.
x=42 ANS.

Answer 6

First, I would isolate the x term on one side, so subtract 6x from both sides

-5x = -210

To solve for x, simply divide each side by -5.

x = 42

Answer 7

x=6x-210
->210=6x-x
->210=5x
->210/5=x
x=42

Which as we all know from Douglas Adams is the answer the "THE QUESTION".

Answer 8

sub. 6x for both sides itll be -5x=-210 then you divide by -5 on each side

Answer 9

First get all the x's one side

-5x=-210

Then you're able to solve for x by division

x=42

Answer 10

x=6x-210
210=6x-x
210=5x
x=42