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Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x-8). Express your answer in interval notation.

 Jun 27, 2022
 #1
avatar+117735 
+1

 (2x+10)(x+3)<(3x+9)(x-8).

 

So what have you done towards solving this???

 

I might start by expanding both sides.

 

Do something yourself and get back to us if you still have problems.

 Jun 27, 2022
 #2
avatar+2222 
0

Here, I'll make your life a little bit easier:

 

We have: \((2x+10)(x+3)<(3x+9)(x-8)\)

 

Now, factor \(3x + 9\)\((2x + 10)( x+3) < 3(x + 3)(x-8)\)

 

Note that because both sides have an \(x + 3\), we can cancel them, giving us \(2x + 10 < 3(x-8)\).

 

To finish, solve it like you would a regular equation, but make sure the sign( < or >) satisfies the equation. 

 Jun 27, 2022
 #3
avatar+117735 
+1

Please do not 'make people's lives easier' by answering over me Builderboi.

If guest had have got back with some suggestion of doing some work for themselves then by all means, help some more.

But I asked thei guest to come back and show that they had done something for themselves and I do not want other answerers answering over me.

 

 

Note:

If I ever answer over you and you  take exception to what I have done then by all means tell me that you are not happy.

I do not expect this to be a one way street.

 

Anyway, yoiu cannot just cancel out x+3 because sometimes it is negative and somteimes it is positive.

Melody  Jun 27, 2022
edited by Melody  Jun 27, 2022
 #4
avatar+2222 
0

Sorry Melody! I won't do it again. smiley

BuilderBoi  Jun 27, 2022
 #5
avatar+117735 
0

Thanks Builderboi  smiley

Melody  Jun 28, 2022

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