SOLUTION: ax+ b = c solve for x

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Question 1203395: ax+ b = c solve for x

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

ax means "a times x"
Adjacent letters together like this usually indicates multiplication.


We start with some unknown number x.
We then multiply it with 'a' to get ax
Then add on b to get ax+b

The order of this is important because we follow those operations in reverse to undo them. This will isolate x.

How do we undo the "add b" part? By subtracting b from both sides.
Undoing the "multiply by a" part means we divide both sides by 'a'.
These are called inverse operations.

Here are the steps to isolate x.


Subtracted b from both sides



Divide both sides by 'a' (we must require that to avoid division by zero errors)

And we're done. The x is all by itself now.

----------------------------------


Here's a slightly more concrete example

Say we had 2x+5 = 37 as our equation.
I replaced 'a' with 2, replaced b with 5, and c with 37.
Pick any three numbers you want. As long as 'a' is nonzero.

We'll subtract 5 from both sides to undo the "plus 5".
Then divide both sides by 2 to undo the "multiply by 2".
Follow PEMDAS in reverse to isolate the variable.



Subtract 5 from both sides



Divided both sides by 2



I'll leave the right hand side unevaluated so you can see how it fits the format

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
ax + b = c solve for x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Three cases may happen:


    (a) no solutions;

    (b) infinitely many solutions;

    (c) one and only one solution.


Case (a) happens when a= 0, b =/= c.

Case (b) happens when a= 0, b = c.

Case (c) happens when a =/= 0,  while b and c may have arbitrary values.


In this case,  x =  is the unique solution.

Solved and explained.



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