Solve 2x-1/3-x+5/6=3x-1/2-2x+9/12

$$\frac { 2 x - 1 } { 3 } - \frac { x + 5 } { 6 } = \frac { 3 x - 1 } { 2 } - \frac { 2 x + 9 } { 12 }$$

Solve for x

$$x=\frac{1}{10}=0.1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,6,2,12.

$$4\left(2x-1\right)-2\left(x+5\right)=6\left(3x-1\right)-\left(2x+9\right)$$

Use the distributive property to multiply 4 by 2x-1.

$$8x-4-2\left(x+5\right)=6\left(3x-1\right)-\left(2x+9\right)$$

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

$$8x-4-2x-10=6\left(3x-1\right)-\left(2x+9\right)$$

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

$$6x-4-10=6\left(3x-1\right)-\left(2x+9\right)$$

Subtract 10 from -4 to get -14.

$$6x-14=6\left(3x-1\right)-\left(2x+9\right)$$

Use the distributive property to multiply 6 by 3x-1.

$$6x-14=18x-6-\left(2x+9\right)$$

To find the opposite of 2x+9, find the opposite of each term.

$$6x-14=18x-6-2x-9$$

Combine 18x and -2x to get 16x.

$$6x-14=16x-6-9$$

Subtract 9 from -6 to get -15.

$$6x-14=16x-15$$

Subtract 16x from both sides.

$$6x-14-16x=-15$$

Combine 6x and -16x to get -10x.

$$-10x-14=-15$$

Add 14 to both sides.

$$-10x=-15+14$$

Add -15 and 14 to get -1.

$$-10x=-1$$

Divide both sides by -10.

$$x=\frac{-1}{-10}$$

Fraction \frac{-1}{-10} can be simplified to \frac{1}{10} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{10}$$