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

1 Answer

Answer:

#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).