Solve x/6-x-1/2=x-13/9

$$\frac { x } { 6 } - \frac { x - 1 } { 2 } = \frac { x - 13 } { 9 }$$

Solve for x

$$x = \frac{35}{8} = 4\frac{3}{8} = 4.375$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 6,2,9.

$$3x-9\left(x-1\right)=2\left(x-13\right)$$

Use the distributive property to multiply -9 by x-1.

$$3x-9x+9=2\left(x-13\right)$$

Combine 3x and -9x to get -6x.

$$-6x+9=2\left(x-13\right)$$

Use the distributive property to multiply 2 by x-13.

$$-6x+9=2x-26$$

Subtract 2x from both sides.

$$-6x+9-2x=-26$$

Combine -6x and -2x to get -8x.

$$-8x+9=-26$$

Subtract 9 from both sides.

$$-8x=-26-9$$

Subtract 9 from -26 to get -35.

$$-8x=-35$$

Divide both sides by -8.

$$x=\frac{-35}{-8}$$

Fraction \frac{-35}{-8} can be simplified to \frac{35}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{35}{8}$$