Solve 5(x-1)-x(7-x)<x^2

$$5 ( x - 1 ) - x ( 7 - x ) < x ^ { 2 }$$

Solve for x

$$x>-\frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 5 by x-1.

$$5x-5-x\left(7-x\right)<x^{2}$$

Use the distributive property to multiply x by 7-x.

$$5x-5-\left(7x-x^{2}\right)<x^{2}$$

To find the opposite of 7x-x^{2}, find the opposite of each term.

$$5x-5-7x+x^{2}<x^{2}$$

Combine 5x and -7x to get -2x.

$$-2x-5+x^{2}<x^{2}$$

Subtract x^{2} from both sides.

$$-2x-5+x^{2}-x^{2}<0$$

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

$$-2x-5<0$$

Add 5 to both sides. Anything plus zero gives itself.

$$-2x<5$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>-\frac{5}{2}$$