Solve 1-x/6-1+x/2+10x-1/16=x

$$\frac { 1 - x } { 6 } - \frac { 1 + x } { 2 } + \frac { 10 x - 1 } { 16 } = x$$

Solve for x

$$x=-\frac{19}{50}=-0.38$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2 is 6. Multiply \frac{1+x}{2} times \frac{3}{3}.

$$\frac{1-x}{6}-\frac{3\left(1+x\right)}{6}+\frac{10x-1}{16}=x$$

Since \frac{1-x}{6} and \frac{3\left(1+x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-x-3\left(1+x\right)}{6}+\frac{10x-1}{16}=x$$

Do the multiplications in 1-x-3\left(1+x\right).

$$\frac{1-x-3-3x}{6}+\frac{10x-1}{16}=x$$

Combine like terms in 1-x-3-3x.

$$\frac{-2-4x}{6}+\frac{10x-1}{16}=x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 16 is 48. Multiply \frac{-2-4x}{6} times \frac{8}{8}. Multiply \frac{10x-1}{16} times \frac{3}{3}.

$$\frac{8\left(-2-4x\right)}{48}+\frac{3\left(10x-1\right)}{48}=x$$

Since \frac{8\left(-2-4x\right)}{48} and \frac{3\left(10x-1\right)}{48} have the same denominator, add them by adding their numerators.

$$\frac{8\left(-2-4x\right)+3\left(10x-1\right)}{48}=x$$

Do the multiplications in 8\left(-2-4x\right)+3\left(10x-1\right).

$$\frac{-16-32x+30x-3}{48}=x$$

Combine like terms in -16-32x+30x-3.

$$\frac{-19-2x}{48}=x$$

Divide each term of -19-2x by 48 to get -\frac{19}{48}-\frac{1}{24}x.

$$-\frac{19}{48}-\frac{1}{24}x=x$$

Subtract x from both sides.

$$-\frac{19}{48}-\frac{1}{24}x-x=0$$

Combine -\frac{1}{24}x and -x to get -\frac{25}{24}x.

$$-\frac{19}{48}-\frac{25}{24}x=0$$

Add \frac{19}{48} to both sides. Anything plus zero gives itself.

$$-\frac{25}{24}x=\frac{19}{48}$$

Multiply both sides by -\frac{24}{25}, the reciprocal of -\frac{25}{24}.

$$x=\frac{19}{48}\left(-\frac{24}{25}\right)$$

Multiply \frac{19}{48} times -\frac{24}{25} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\left(-24\right)}{48\times 25}$$

Do the multiplications in the fraction \frac{19\left(-24\right)}{48\times 25}.

$$x=\frac{-456}{1200}$$

Reduce the fraction \frac{-456}{1200} to lowest terms by extracting and canceling out 24.

$$x=-\frac{19}{50}$$