Question 1203395
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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.
{{{ax + b = c}}}


{{{ax + b-b = c-b}}} Subtracted b from both sides


{{{ax = c-b}}}


{{{ax/a = (c-b)/a}}} Divide both sides by 'a' (we must require that {{{a <> 0}}} to avoid division by zero errors)


{{{x = (c-b)/a}}} And we're done. The x is all by itself now.


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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. 


{{{2x + 5 = 37}}}


{{{2x + 5-5 = 37-5}}} Subtract 5 from both sides


{{{2x = 37-5}}}


{{{2x/2 = (37-5)/2}}} Divided both sides by 2


{{{x = (37-5)/2}}}


I'll leave the right hand side unevaluated so you can see how it fits the format {{{(c-b)/a}}} 
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