Solve (x-1)^2-(x-2)^2/2+x-1/2=1-x/6

$$\frac { ( x - 1 ) ^ { 2 } - ( x - 2 ) ^ { 2 } } { 2 } + \frac { x - 1 } { 2 } = \frac { 1 - x } { 6 }$$

Solve for x

$$x = \frac{13}{10} = 1\frac{3}{10} = 1.3$$

Steps for Solving Linear Equation

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

$$3\left(\left(x-1\right)^{2}-\left(x-2\right)^{2}\right)+3\left(x-1\right)=1-x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$3\left(x^{2}-2x+1-\left(x-2\right)^{2}\right)+3\left(x-1\right)=1-x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$3\left(x^{2}-2x+1-\left(x^{2}-4x+4\right)\right)+3\left(x-1\right)=1-x$$

To find the opposite of x^{2}-4x+4, find the opposite of each term.

$$3\left(x^{2}-2x+1-x^{2}+4x-4\right)+3\left(x-1\right)=1-x$$

Combine x^{2} and -x^{2} to get 0.

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

Combine -2x and 4x to get 2x.

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

Subtract 4 from 1 to get -3.

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

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

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

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

$$6x-9+3x-3=1-x$$

Combine 6x and 3x to get 9x.

$$9x-9-3=1-x$$

Subtract 3 from -9 to get -12.

$$9x-12=1-x$$

Add x to both sides.

$$9x-12+x=1$$

Combine 9x and x to get 10x.

$$10x-12=1$$

Add 12 to both sides.

$$10x=1+12$$

Add 1 and 12 to get 13.

$$10x=13$$

Divide both sides by 10.

$$x=\frac{13}{10}$$