Solve 1-2x-1/6=2x-x-1/3

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

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps for Solving Linear Equation

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

$$6-\left(2x-1\right)=12x-2\left(x-1\right)$$

To find the opposite of 2x-1, find the opposite of each term.

$$6-2x-\left(-1\right)=12x-2\left(x-1\right)$$

The opposite of -1 is 1.

$$6-2x+1=12x-2\left(x-1\right)$$

Add 6 and 1 to get 7.

$$7-2x=12x-2\left(x-1\right)$$

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

$$7-2x=12x-2x+2$$

Combine 12x and -2x to get 10x.

$$7-2x=10x+2$$

Subtract 10x from both sides.

$$7-2x-10x=2$$

Combine -2x and -10x to get -12x.

$$7-12x=2$$

Subtract 7 from both sides.

$$-12x=2-7$$

Subtract 7 from 2 to get -5.

$$-12x=-5$$

Divide both sides by -12.

$$x=\frac{-5}{-12}$$

Fraction \frac{-5}{-12} can be simplified to \frac{5}{12} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{12}$$