Solve x-2/4-x+5/6=5x-2/9

$$\frac { x - 2 } { 4 } - \frac { x + 5 } { 6 } = \frac { 5 x - 2 } { 9 }$$

Solve for x

$$x = -\frac{40}{17} = -2\frac{6}{17} \approx -2.352941176$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 4,6,9.

$$9\left(x-2\right)-6\left(x+5\right)=4\left(5x-2\right)$$

Use the distributive property to multiply 9 by x-2.

$$9x-18-6\left(x+5\right)=4\left(5x-2\right)$$

Use the distributive property to multiply -6 by x+5.

$$9x-18-6x-30=4\left(5x-2\right)$$

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

$$3x-18-30=4\left(5x-2\right)$$

Subtract 30 from -18 to get -48.

$$3x-48=4\left(5x-2\right)$$

Use the distributive property to multiply 4 by 5x-2.

$$3x-48=20x-8$$

Subtract 20x from both sides.

$$3x-48-20x=-8$$

Combine 3x and -20x to get -17x.

$$-17x-48=-8$$

Add 48 to both sides.

$$-17x=-8+48$$

Add -8 and 48 to get 40.

$$-17x=40$$

Divide both sides by -17.

$$x=\frac{40}{-17}$$

Fraction \frac{40}{-17} can be rewritten as -\frac{40}{17} by extracting the negative sign.

$$x=-\frac{40}{17}$$