Solve the Inequality for x -X^2+4x-7<0

$- X^{2} + 4 x - 7 < 0$

Move all terms not containing $x$ to the right side of the inequality.

Add $X^{2}$ to both sides of the inequality.

$4 x - 7 < X^{2}$

Add $7$ to both sides of the inequality.

$4 x < X^{2} + 7$

Divide each term in $4 x < X^{2} + 7$ by $4$ and simplify.

Divide each term in $4 x < X^{2} + 7$ by $4$ .

$\frac{4 x}{4} < \frac{X^{2}}{4} + \frac{7}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{X^{2}}{4} + \frac{7}{4}$

Divide $x$ by $1$ .

$x < \frac{X^{2}}{4} + \frac{7}{4}$