Question

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

Answer 1

`x>1`

Explanation:

We start with:

`x^2+1<2x`

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^2-2x+1=0`

`(x-1)(x-1)=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<2x`

`0+1<2(0)`

`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).