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

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

Solve for x

$$x<1$$

Solution Steps

Use the distributive property to multiply 3-2x by 2-x and combine like terms.

$$x^{2}-1<6-7x+2x^{2}-x^{2}$$

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

$$x^{2}-1<6-7x+x^{2}$$

Add 7x to both sides.

$$x^{2}-1+7x<6+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-1+7x-x^{2}<6$$

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

$$-1+7x<6$$

Add 1 to both sides.

$$7x<6+1$$

Add 6 and 1 to get 7.

$$7x<7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x<\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$x<1$$