```Question 202227
Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.

(x+4)/3 + (x - 8)/7 = 4/21

Just like in adding regular fractions, you have to find a common denominator. In this case, your common denominator should be 21........

So in the first part of the equation, (x+4)/3, you ask yourself:  How many times does 3 go into 21?  The answer is 7, so you multiply like this:  7(X+4)/21

Now in the 2nd part of the equation, (x -8)/7, you ask yourself:  How many times does 7 go into 21?  The answer is 3, so you multiply like this:  3(x-8)/21

SO now you have:

7(x+4)/21 + 3(x-8)/21 = 4/21

You can get rid of the denominator by multiplying both sides by 21/1.  That makes your equation this:

7(x+4) + 3(x-8) = 4   Now solve!
7x + 28 + 3x - 24 = 4  (distributed the 7 and the 3)
10x + 4 = 4 (combined like terms. 7x+3x = 10x and 28 - 24 = 4)
10x = 4 - 4 (subtracted 4 from both sides)
10x = 0

X = 0 (divided both sides by 10)

Now let's plug in "0" in every place where we have an "x'...........

(x+4)/3 + (x - 8)/7 = 4/21  (original equation)

(0 +4)/3 + (0 -8)/7 = 4/21

{{{4/3  -8/7 = 4/21}}}
{{{28/21 - 24/21 = 4/21}}}
{{{4/21 = 4/21}}}

Yay!  It works.
I hope this was helpful. :-)```