SOLUTION: I need help with rearranging an equation. Can you please show a step by step method of how to get to the value of x. Thank you. 1600= 192/(0.12-x)-600

Question 1105493: I need help with rearranging an equation. Can you please show a step by step method of how to get to the value of x. Thank you.
1600= 192/(0.12-x)-600
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Think of the fraction 192/(0.12-x) as the variable z.

So we'll say z = 192/(0.12-x)

Allowing us to go from this
1600 = 192/(0.12-x) - 600
to this
1600 = z - 600

At this point, you hopefully agree that this new equation is much easier to deal with. The sub-goal here is to solve for z. To do so, we undo the subtraction done to z by adding. We add 600 to both sides

1600 = z - 600
1600+600 = z - 60+600
2200 = z
z = 2200

We found the solution for z, but what we really want is the solution for x. So we need to get z back into terms of x. Replace z with the fraction written in blue above. So we'll replace z with 192/(0.12-x)

We go from this
z = 2200
to this
192/(0.12-x) = 2200

Think of the 2200 on the right side as 2200/1. So we really have this equation
192/(0.12-x) = 2200/1

Now we cross multiply
192/(0.12-x) = 2200/1
192*1 = 2200(0.12-x)
192 = 2200(0.12-x)

Next we distribute the 2200 through to each term inside the parenthesis
192 = 2200(0.12-x)
192 = 2200(0.12)+2200(-x)
192 = 264-2200x

From here, we treat this as any other linear equation to solve
192 = 264-2200x
264-2200x = 192
-2200x+264 = 192
-2200x+264-264 = 192-264 ... subtract 264 from both sides
-2200x = -72
-2200x/(-2200) = -72/(-2200) ... divide both sides by -2200
x = 72/2200
x = (8*9)/(8*275)
x = 9/275 <<--- Exact Answer as a fraction
x = 0.032727 <<--- Approximate Answer in decimal form(accurate to 6 decimal places; the '27' repeats forever)

The answer format (either exact or approximate) will depend on what your teacher wants.

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