3. Solve for x and check

 

(ax+b)/c=x

First we need to clear denominators. Multiply both sides by c.

 

ax + b = cx

 

Transpose known terms to one side and unknown terms to the

other. The simplest way to get all of the x terms together on the

same side of the equation would be to transpose the ax to the right.

 

b = cx-ax

 

To get the x's altogether in one place, factor an x out of the two

terms on the left side of the equation.

 

b=(c-a)x

 

Now, we need only divide both sides by the coefficient of x.

 

b/(c-a)=x

 

If a = c, then we will have a zero denominator, and the

expression will not give us a solution. In this case, if b = 0, then so

long as c is not 0 any value of x will give us a solution. Otherwise,

there will be no real solution.

 

 

Check

Copy down the original equation

 

(ax+b)/c=x

 

except, where you see an x, substitute the solution in parentheses.

 

(a(b/(c-a))+b)/c= (b/(c-a))

 

On the top of the left side we are adding fractions, so we need

to find common denominators.

 

(a(b/(c-a))+b((c-a)/(c-a)))/c= (b/(c-a))

 

Remove parentheses.

 

(ab/(c-a)+(bc-ba)/(c-a)))/c= (b/(c-a))

 

Now that we have common denominators on the top of the

right, we can add the fractions.

 

((ab+bc-ba)/(c-a))/c= (b/(c-a))

 

this simplifies to

 

(bc/(c-a))/c= (b/(c-a))

 

If we invert and multiply, we get

 

bc/(c-a)(1/c)= b/(c-a)

 

or

 

b/(c-a)=b/(c-a)

 

and it checks.

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