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

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

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

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

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

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

The opposite of -1 is 1.

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

Add 6 and 1 to get 7.

$$7-x=3x+2\left(x-1\right)$$

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

$$7-x=3x+2x-2$$

Combine 3x and 2x to get 5x.

$$7-x=5x-2$$

Subtract 5x from both sides.

$$7-x-5x=-2$$

Combine -x and -5x to get -6x.

$$7-6x=-2$$

Subtract 7 from both sides.

$$-6x=-2-7$$

Subtract 7 from -2 to get -9.

$$-6x=-9$$

Divide both sides by -6.

$$x=\frac{-9}{-6}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.

$$x=\frac{3}{2}$$