Question

x
$x - \frac{2x + 8}{3} = \frac{1}{4} (x - \frac{2 - x}{6 }) - 3$
solve:

Answer 1

Thanks for A2A.

First step is to find the domain of . We know that denominator can't be zero, so  and we get that domain for this equation is 

Second step is to find LCM for the denominators of every term.

You can rewrite the equation as:

Now we can see the LCM for denominators is 

Next step is to multiple every term of the equation with  and we get:

Next we solve this for  and we get

.

Now we check if , which is true, so the solution of the equation is

.

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Answer 2

Your answer is here ↙↙↙↘↘↘↘↙↘↙↙

$\frac{ 3x - 2x + 8}{3 } = \frac{1}{4} (x - \frac{2 - x}{6} ) - 3 \\ \\ \frac{x + 8}{3} = \frac{1}{4} ( \frac{5x - 2}{6} ) - 3 \\ \\ \frac{x + 8}{3} = \frac{5x - 2}{24} - 3 \\ \\ \frac{x + 8}{3} = \frac{5x - 2 - 72}{24 } \\ \\ \frac{x + 8}{3 } = \frac{5x - 74}{24} \\ \\ 24(x + 8) = 3(5x - 74) \\ \\ 24x + 192 = 15x - 222 \\ \\ 24x - 15x = - 222 - 192 \\ \\ 9x = - 414 \\ \\ x = \frac{ - 414}{9} \\ \\ x = - 46$