Solve 1/4+(2x-3x-1/8)=2/3(x+2/6)-2x

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

Solve for x

$$x=-\frac{1}{23}\approx -0.043478261$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 4,8,3,6.

$$6+48x-3\left(3x-1\right)=\frac{8}{3}\left(x+2\right)-48x$$

Use the distributive property to multiply -3 by 3x-1.

$$6+48x-9x+3=\frac{8}{3}\left(x+2\right)-48x$$

Combine 48x and -9x to get 39x.

$$6+39x+3=\frac{8}{3}\left(x+2\right)-48x$$

Add 6 and 3 to get 9.

$$9+39x=\frac{8}{3}\left(x+2\right)-48x$$

Use the distributive property to multiply \frac{8}{3} by x+2.

$$9+39x=\frac{8}{3}x+\frac{8}{3}\times 2-48x$$

Express \frac{8}{3}\times 2 as a single fraction.

$$9+39x=\frac{8}{3}x+\frac{8\times 2}{3}-48x$$

Multiply 8 and 2 to get 16.

$$9+39x=\frac{8}{3}x+\frac{16}{3}-48x$$

Combine \frac{8}{3}x and -48x to get -\frac{136}{3}x.

$$9+39x=-\frac{136}{3}x+\frac{16}{3}$$

Add \frac{136}{3}x to both sides.

$$9+39x+\frac{136}{3}x=\frac{16}{3}$$

Combine 39x and \frac{136}{3}x to get \frac{253}{3}x.

$$9+\frac{253}{3}x=\frac{16}{3}$$

Subtract 9 from both sides.

$$\frac{253}{3}x=\frac{16}{3}-9$$

Convert 9 to fraction \frac{27}{3}.

$$\frac{253}{3}x=\frac{16}{3}-\frac{27}{3}$$

Since \frac{16}{3} and \frac{27}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{253}{3}x=\frac{16-27}{3}$$

Subtract 27 from 16 to get -11.

$$\frac{253}{3}x=-\frac{11}{3}$$

Multiply both sides by \frac{3}{253}, the reciprocal of \frac{253}{3}.

$$x=-\frac{11}{3}\times \frac{3}{253}$$

Multiply -\frac{11}{3} times \frac{3}{253} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\times 3}{3\times 253}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{-11}{253}$$

Reduce the fraction \frac{-11}{253} to lowest terms by extracting and canceling out 11.

$$x=-\frac{1}{23}$$