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Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x+18). Express your answer in interval notation.

 Apr 20, 2022

Best Answer 

 #1
avatar+1370 
+2

Expanding the quadratic, we get: \(2x^2+16x+30 <3x^2+63x+162\)

 

Bringing everything to the left-hand side, we get: \(-x^2-47x-132<0\)

 

Multiply through by -1 to make all the coefficients positive: \(x^2+47x+132>0\) (Remember to switch the sign, because we multiplied by a negative!!)

 

Factoring this equation, we get: \((x+44)(x+3)>0\)

 

For the result to be positive, we either need: \(\text{pos} \times \text{pos}\) or \(\text{neg} \times \text{neg}\).

 

You can do the rest from here, right?

 Apr 20, 2022
 #1
avatar+1370 
+2
Best Answer

Expanding the quadratic, we get: \(2x^2+16x+30 <3x^2+63x+162\)

 

Bringing everything to the left-hand side, we get: \(-x^2-47x-132<0\)

 

Multiply through by -1 to make all the coefficients positive: \(x^2+47x+132>0\) (Remember to switch the sign, because we multiplied by a negative!!)

 

Factoring this equation, we get: \((x+44)(x+3)>0\)

 

For the result to be positive, we either need: \(\text{pos} \times \text{pos}\) or \(\text{neg} \times \text{neg}\).

 

You can do the rest from here, right?

BuilderBoi Apr 20, 2022
 #2
avatar+125 
-3

Have you seen vin latley

Kakashi  Apr 20, 2022
 #3
avatar+1370 
+1

unfortunately not.

BuilderBoi  Apr 20, 2022

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