Solve x-1/3=x-2/4+2x-5/6

$$\frac{ x-1 }{ 3 } = \frac{ x-2 }{ 4 } + \frac{ 2x-5 }{ 6 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$4\left(x-1\right)=3\left(x-2\right)+2\left(2x-5\right)$$

Use the distributive property to multiply 4 by x-1.

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

Use the distributive property to multiply 3 by x-2.

$$4x-4=3x-6+2\left(2x-5\right)$$

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

$$4x-4=3x-6+4x-10$$

Combine 3x and 4x to get 7x.

$$4x-4=7x-6-10$$

Subtract 10 from -6 to get -16.

$$4x-4=7x-16$$

Subtract 7x from both sides.

$$4x-4-7x=-16$$

Combine 4x and -7x to get -3x.

$$-3x-4=-16$$

Add 4 to both sides.

$$-3x=-16+4$$

Add -16 and 4 to get -12.

$$-3x=-12$$

Divide both sides by -3.

$$x=\frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$x=4$$