Solve 2x-1/9-x-4/5=x

$$\frac{ 2x-1 }{ 9 } - \frac{ x-4 }{ 5 } =x$$

Solve for x

$$x=\frac{31}{44}\approx 0.704545455$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 5 is 45. Multiply \frac{2x-1}{9} times \frac{5}{5}. Multiply \frac{x-4}{5} times \frac{9}{9}.

$$\frac{5\left(2x-1\right)}{45}-\frac{9\left(x-4\right)}{45}=x$$

Since \frac{5\left(2x-1\right)}{45} and \frac{9\left(x-4\right)}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(2x-1\right)-9\left(x-4\right)}{45}=x$$

Do the multiplications in 5\left(2x-1\right)-9\left(x-4\right).

$$\frac{10x-5-9x+36}{45}=x$$

Combine like terms in 10x-5-9x+36.

$$\frac{x+31}{45}=x$$

Divide each term of x+31 by 45 to get \frac{1}{45}x+\frac{31}{45}.

$$\frac{1}{45}x+\frac{31}{45}=x$$

Subtract x from both sides.

$$\frac{1}{45}x+\frac{31}{45}-x=0$$

Combine \frac{1}{45}x and -x to get -\frac{44}{45}x.

$$-\frac{44}{45}x+\frac{31}{45}=0$$

Subtract \frac{31}{45} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{44}{45}x=-\frac{31}{45}$$

Multiply both sides by -\frac{45}{44}, the reciprocal of -\frac{44}{45}.

$$x=-\frac{31}{45}\left(-\frac{45}{44}\right)$$

Multiply -\frac{31}{45} times -\frac{45}{44} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-31\left(-45\right)}{45\times 44}$$

Do the multiplications in the fraction \frac{-31\left(-45\right)}{45\times 44}.

$$x=\frac{1395}{1980}$$

Reduce the fraction \frac{1395}{1980} to lowest terms by extracting and canceling out 45.

$$x=\frac{31}{44}$$