Question

Solve the following inequality (step-by-step):
$x-2(5-2x)\geq 6x-3 \frac{1}{2}$

Answer 1

Step-by-step explanation:

(6x−5)∣ln(2x−2.3)∣=8ln(2x+2.3)

We know that ln x>0∀x>1

and lnx<0∀

0

<x<1

∴(6x−5)∣ln(2x+2.3)∣=8ln(2x+2.3)

case I :

If 2x+2.3>1

⇒x≥−1.3/2

⇒x≥−13/20, then

(6x−5)ln(2x+2.3)−8ln(2x+2.3)=0

⇒ln(2x+2.3)[6x−13]=0

∴ln(2x+2.3)=0 or 6x−13=0

⇒2x+2.3=1 or x=13/6

x=−13/20 or x=13/6

case 2 :

if 2x+2.3<1⇒x<−13/20 then

−(6x−5)ln(2x+2.3)−8ln(2x+2.3)=0

⇒ln(2x+2.3)(6x+3)=0

∴ln(2x+2.3)=0 = or 6x+3=0

2x+2.3=1 or x=−1/2

x=−13/20

However in the case 2 the allowed region is a<−13/20

Hence x=−13/20 & −1/2 are not permissible

∴x=−13/20 & x=13/6 are the only solution possible