Question

if (x+3)/(x-2)>1/2 then x lies in the interval​

Answer 1

Step-by-step explanation:

x+3 1

___ > __

x-2 2

cross multiply the given inequality

=> 2(x+3) >x-2

2x+6 > x-2

2x-x > -2-6

x > -8

x lies between (-8, + infinity)

Answer 2

Given,

$\frac{x+3}{x-2} > \frac{1}{2}$

To find,

The interval in which x lies.

Solution,

The interval in which x lies is x ⊆ { x > -8 , x⊄ {-3,} }

We can simply solve the mathematical problem by the following process.

We know that,

∴ $\frac{x+3}{x-2} > \frac{1}{2}$

⇒ 2(x+3) > x-2

⇒ 2x - x > -2 -6

⇒ x > -8

The interval in which x lies is x ⊆ { x > -8 , x⊄ {-3,} }

Note: We exclude the value of x as -3 as if it is put in the original inequality, it would not follow the inequality.