Solve 4x-6/12-3x-8/4=2x-9/6-x-4/8

$$\frac { 4 x - 6 } { 12 } - \frac { 3 x - 8 } { 4 } = \frac { 2 x - 9 } { 6 } - \frac { x - 4 } { 8 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 12,4,6,8.

$$2\left(4x-6\right)-6\left(3x-8\right)=4\left(2x-9\right)-3\left(x-4\right)$$

Use the distributive property to multiply 2 by 4x-6.

$$8x-12-6\left(3x-8\right)=4\left(2x-9\right)-3\left(x-4\right)$$

Use the distributive property to multiply -6 by 3x-8.

$$8x-12-18x+48=4\left(2x-9\right)-3\left(x-4\right)$$

Combine 8x and -18x to get -10x.

$$-10x-12+48=4\left(2x-9\right)-3\left(x-4\right)$$

Add -12 and 48 to get 36.

$$-10x+36=4\left(2x-9\right)-3\left(x-4\right)$$

Use the distributive property to multiply 4 by 2x-9.

$$-10x+36=8x-36-3\left(x-4\right)$$

Use the distributive property to multiply -3 by x-4.

$$-10x+36=8x-36-3x+12$$

Combine 8x and -3x to get 5x.

$$-10x+36=5x-36+12$$

Add -36 and 12 to get -24.

$$-10x+36=5x-24$$

Subtract 5x from both sides.

$$-10x+36-5x=-24$$

Combine -10x and -5x to get -15x.

$$-15x+36=-24$$

Subtract 36 from both sides.

$$-15x=-24-36$$

Subtract 36 from -24 to get -60.

$$-15x=-60$$

Divide both sides by -15.

$$x=\frac{-60}{-15}$$

Divide -60 by -15 to get 4.

$$x=4$$