How do you solve #6/x+2>=0# using a sign chart?

1 Answer
Nov 9, 2016

Answer:

#x<=-3, x>=0#

Explanation:

First solve the inequality as if it were an equality:

#6/x+2=0#

#6/x+(2x)/x=0#

#[2(x+3)]/[x]=0#

Set the numerator equal to zero to find where the function intersects the x axis and changes signs, and set the denominator equal to zero to find where the function has an asymptote and (possibly) changes signs.

Numerator:
#x=-3#

Denominator:
#x=0#

Now put the values on a number line and test values around them, and check if they are positive or negative.
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The question asks where is the function greater than or equal to 0, so, the answer is:
#x<=-3, x>=0#