solve

x+21/x+3<2

x+21/x+3 - 2(x+3)/x+3 <0
x+21-2(x-3)/x+3<0
x+21-2x-6/x+3<0
answer
15-x/x-3<0(is this right?)

For Further Reading

Algebra - Anonymous, Thursday, April 3, 2008 at 5:07pm
You are close. They want you to find the values of x so that the equation the inequality is true. So just do that and you have your answer. I'll be happy to check you answer again when you are done.

Just a note. When you are writing fractions horizontally, you have to put parenthesis around the numerator and the denominator. Otherwise like for your x+21/x+3
It's the same as x + (21/x) + 3. The proper way to do it is (x+21)/(x+3) but anyways its very minor and you probably don't right fractions horizontally in real life, normally.

Algebra - Cynthia, Thursday, April 3, 2008 at 10:31pm

Is this right?
(15-x)/(x-3)<0
15-x<0
-x<-15
answer is x>15
x+3<0
answer is x<-3

Yes.

To solve the inequality x + 21/(x + 3) < 2, you followed the correct steps in simplifying and getting the expression (15 - x)/(x - 3) < 0. However, you made a mistake in the next step.

The correct steps are:

1. x + 21/(x + 3) < 2
2. Multiply both sides of the inequality by (x + 3) to eliminate the denominator: (x + 21) - 2(x + 3) < 0
3. Simplify the expression: x + 21 - 2x - 6 < 0
4. Combine like terms: -x + 15 < 0
5. Multiply both sides of the inequality by -1. Remember that when you multiply or divide both sides of the inequality by a negative number, you must reverse the direction of the inequality: x - 15 > 0
6. Add 15 to both sides: x > 15

So the correct solution is x > 15.

I hope this helps clarify the solution process! Let me know if you have any other questions.