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

1 Answer
MathFact-orials.blogspot.com
Oct 6, 2016

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).

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