Question

can you help me to solve the following inequality:
x^2 >=16

Answer 1

Can you show the work, please?

Answer 2

graph
\[y=x^2-16\] and you will see a parabola that faces up and crosses the x-axis at -4 and 4. from the picture you will see that it is positive if x<-4 or if x> 4

Answer 3

analitically

Answer 4

there is another more complicated way to do this, but if you know what the graph of \[y=x^2-16\] looks like it is simple.

Answer 5

well step number one is going to be to write
\[x^2-16\geq0\]

Answer 6

so you are going to have to work with that in any case. you cannot, for example, take the square root of both sides.

Answer 7

I need to do it analitically

Answer 8

then you can factor
\[x^2-16=(x+4)(x-4)\geq 0\]

Answer 9

got it

Answer 10

Im such a fool

Answer 11

then you can look at the sign of each factor. yes?

Answer 12

you are still going to get
positive, negative, positive on
\[(-\infty,-4), (-4,4), (4,\infty) \] respectively

Answer 13

thanks

Answer 14

welcome