SOLUTION: Solve the inequality. State the answer in interval notation. 4/(x+1) <_ 3/(x+2) the symbol in the middle is supposed to mean "less than or equal to". So far I've multiplied

Algebra ->  Inequalities -> SOLUTION: Solve the inequality. State the answer in interval notation. 4/(x+1) <_ 3/(x+2) the symbol in the middle is supposed to mean "less than or equal to". So far I've multiplied      Log On


   

Question 890782: Solve the inequality. State the answer in interval notation.
4/(x+1) <_ 3/(x+2)
the symbol in the middle is supposed to mean "less than or equal to". So far I've multiplied both sides by (x+1) and (x+2) to try and get rid of the fraction.
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Put all the expressions onto one side.

Note the critical values of x at -1 and -2.

4%2F%28x%2B1%29-3%2F%28x%2B2%29=0, CHECK THE EQUALITY. This may be another critical value.

Multiply both sides by LCD.
4%28x%2B2%29-3%28x%2B1%29=0
4x%2B8-3x-3=0
x%2B5=0
x=-5, possibly another critical point along with -1 and -2.

Look for truth or falseness in the intervals for 4%2F%28x%2B1%29%3C=3%2F%28x%2B2%29.
x<=-5
4%2F%28-6%2B1%29%3C3%2F%28-6%2B2%29
-4%2F5%3C-3%2F4, TRUE.
4%2F%28-5%2B1%29%3C3%2F%28-5%2B2%29
-1%3C-1%7D%7D%2C+FALSE.++%7B%7B%7Bx%3C-5.
-5<=x<=-2
4%2F%28-3%2B1%29%3C3%2F%28-3%2B2%29
-2%3C-3%2F2, TRUE.
4%2F%28-2%2B1%29%3C3%2F%28-2%2B2%29, FALSE. x%3C%3E-2.
-2<=x<=-1, x%3C%3E-1.

So far, you know x%3C-5 OR -5%3Cx%3C-2----- still not finished finding solutions for x.


CAN YOU FINISH THESE?
NEED ALSO TO CHECK
-2<=x<=-1, x%3C%3E-1.
-1<=x