SOLUTION: 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 + (

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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
Found 2 solutions by PRMath, RAY100:
Answer by PRMath(133) (Show Source):
You can put this solution on YOUR website!
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

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

Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
(x+4)/3 + (x-8)/7 =4/21
.
{7(x+4) +3(x-8)}/21 =4/21
.
7x+28 +3x -24 =4
.
10x = 0
.
x=0
.
check,,,4/3 -8/7 = 4/21,,,,1.333 - 1.143 =.19,,,,,ok