How do you solve 3−xx+5≤0 using a sign chart?

1 Answer
Shwetank Mauria
Oct 2, 2016

3−xx+5≤0 when either x<−5 or x≥3, which is the solution for the inequality. Note that at x=−5, it is not defined.

Explanation:

The sign of 3−xx+5 depends on the signs of binomials (3−x) and x+5, which should change around the values −5 and 3 respectively. In sign chart we divide the real number line using these values, i.e. below −5, between −5 and 3 and above 3 and see how the sign of 3−xx+5 changes.

Sign Chart

XXXXXXXXXXX−5XXXXX3

(3−x)XXX+iveXXXX+iveXXXX−ive

(x+5)XXX−iveXXXX+iveXXXX+ive

3−xx+5XXX−iveXXXX+iveXXXX−ive

It is observed that 3−xx+5≤0 when either x<−5 or x≥3, which is the solution for the inequality. Note that at x=−5, it is not defined.
graph{(3-x)/(x+5) [-20, 20, -10, 10]}

Related questions
See all questions in Sign Charts
Impact of this question
1952 views around the world
You can reuse this answer
Creative Commons License