What is the answer to 3/4 cbx-1/2 b= 1/2 bx-1/8 cx+(cb)/4 ?

The answer to 3/4 cbx-1/2 b= 1/2 bx-1/8 cx+(cb)/4 is x=(2cb+4b)/(6cb-4b+c);\quad c\ne (4b)/(6b+1)

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3/4 cbx-1/2 b= 1/2 bx-1/8 cx+(cb)/4

\frac{3}{4} c b x - \frac{1}{2} b = \frac{1}{2} b x - \frac{1}{8} c x + \frac{c b}{4}

x = \frac{2 c b + 4 b}{6 c b - 4 b + c}; c \neq = \frac{4 b}{6 b + 1}

Solution steps

\frac{3}{4} c b x - \frac{1}{2} b = \frac{1}{2} b x - \frac{1}{8} c x + \frac{c b}{4}

Move

\frac{1}{2} b

to the right side

\frac{3}{4} c b x = \frac{1}{2} b x - \frac{1}{8} c x + \frac{c b}{4} + \frac{1}{2} b

Subtract

\frac{1}{2} b x - \frac{1}{8} c x

from both sides

\frac{3}{4} c b x - (\frac{1}{2} b x - \frac{1}{8} c x) = \frac{1}{2} b x - \frac{1}{8} c x + \frac{c b}{4} + \frac{1}{2} b - (\frac{1}{2} b x - \frac{1}{8} c x)

Simplify

\frac{3}{4} c b x - \frac{1}{2} b x + \frac{1}{8} c x = \frac{c b}{4} + \frac{1}{2} b

Multiply by LCM

6 c b x - 4 b x + c x = 2 c b + 4 b

Factor

6 c b x - 4 b x + c x : x (6 c b - 4 b + c)

x (6 c b - 4 b + c) = 2 c b + 4 b

Divide both sides by

6 c b - 4 b + c; c \neq = \frac{4 b}{6 b + 1}

x = \frac{2 c b + 4 b}{6 c b - 4 b + c}; c \neq = \frac{4 b}{6 b + 1}

3 (z - 2) + 10 = 2 (2 z + 2) + 2

4 (q - 8) = 7 q + 5

- 14 = \frac{2 ( h - 3 )}{5}

x - 15 = 27

9 x - 15 = 3 x + 21

What is the answer to 3/4 cbx-1/2 b= 1/2 bx-1/8 cx+(cb)/4 ?
The answer to 3/4 cbx-1/2 b= 1/2 bx-1/8 cx+(cb)/4 is x=(2cb+4b)/(6cb-4b+c);\quad c\ne (4b)/(6b+1)