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# Inequality

0
82
3
+309

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

Apr 20, 2022

#1
+2453
+1

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
+2453
+1

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
+115
-4

Have you seen vin latley

Kakashi  Apr 20, 2022
#3
+2453
+1

unfortunately not.

BuilderBoi  Apr 20, 2022