# How do you solve and graph x^2+1<2x?

$x > 1$

#### Explanation:

${x}^{2} + 1 < 2 x$

We'll solve this the same way as if it were an equal sign - so let's drop in an equal sign for now, so:

${x}^{2} - 2 x + 1 = 0$

$\left(x - 1\right) \left(x - 1\right) = 0$ only need to find the one solution, so

$x - 1 = 0$

$x = 1$

Ok - so we know the x value where the two sides are equal. So where are the values of x that satisfy the inequality - are they to the left or to the right of 1? Let's test what happens when $x = 0$:

${x}^{2} + 1 < 2 x$

$0 + 1 < 2 \left(0\right)$

$1 < 0$ - No. So it's not values less than 1 that will work - it's values more than one. So the solution is:

$x > 1$

For the graph, it'll be a ray along the x-axis (or number line) starting at $x = 1$ with a little circle around that point (to indicate that $x = 1$ is not a solution) and the ray pointing to the right (towards larger numbers).