+1671 Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x+18). Express your answer in interval notation.
+2666 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?
+2666 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?
