Solve (x-1)^2-(x-1)^2<-2/3

$$( x - 1 ) ^ { 2 } - ( x - 1 ) ^ { 2 } < - \frac { 2 } { 3 }$$

Evaluate (complex solution)

Solution Steps

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

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

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

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

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$x^{2}-2x+1-x^{2}+2x-1<-\frac{2}{3}$$

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

$$-2x+1+2x-1<-\frac{2}{3}$$

Combine -2x and 2x to get 0.

$$1-1<-\frac{2}{3}$$

Subtract 1 from 1 to get 0.

$$0<-\frac{2}{3}$$

Compare 0 and -\frac{2}{3}.

$$\text{false}$$