Solve x^2-1>x^2-7x+14

$${ x }^{ 2 } -1 > { x }^{ 2 } -7x+14$$

Solve for x

$$x>\frac{15}{7}$$

Solution Steps

Subtract x^{2} from both sides.

$$x^{2}-1-x^{2}>-7x+14$$

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

$$-1>-7x+14$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-7x+14<-1$$

Subtract 14 from both sides.

$$-7x<-1-14$$

Subtract 14 from -1 to get -15.

$$-7x<-15$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>\frac{-15}{-7}$$

Fraction \frac{-15}{-7} can be simplified to \frac{15}{7} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{15}{7}$$