SOLUTION: x+3 divided by x < or equal to -2

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Question 118880This question is from textbook Elementary and Intemediate Algebra
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x+3 divided by x < or equal to -2 This question is from textbook Elementary and Intemediate Algebra

Found 2 solutions by solver91311, checkley71:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%2Fx%3C=-2 (Note that this equation would be undefined for x=0)

Multiply both sides by x

x%2B3%3C=-2x

Add 2x to both sides

x%2B2x%2B3%3C=0

Combine terms

3x%2B3%3C=0

Add -3 to both sides

3x%3C=-3

Multiply both sides by 1%2F3

x%3C=-1

Note that we did not multiply by a negative quantity at any time, so the sense of the inequality (less than or equal) did not change. We also want to make sure that there are no values in the solution set that could cause the rational expression in the original equation to have a zero denominator. In this case we are safe because the only value that would be a problem is x = 0 but that is outside of the solution set interval -infinity%3Cx%3C=-1


Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
(x+3)/x<=-2 cross multiply.
x+3<=-2x
x+2x<=-3
3x<=-3
x<=-3/3
x<=-1 answer.
proof.
let x=-1.1
(-1.1+3)/-1.1<=-2
1.9/-1.1<=-2
-1.72<=-2