Question

Given: -1/2 x > 6.

Choose the solution set.

{x | x R, x > -12}
{x | x R, x < -12}
{x | x R, x > -3}
{x | x R, x < -3}

Answer 1

{x|x R, x is greater than -3

Answer 2

this question is based on concepts of inequalities.

here it is given that -1/2 x > 6

from property of inequality,
if a > b inequality equation is given
then, after multiplying (-1) in both sides of inequality , sign of inequality will be reverse.
e.g., -a < -b

for example ; 4 > 5 but -4 > -5

now come to the equation,
-1/2 x > 6
or, -x/2 > 6
or, x/2 < -6
or, x < -12

hence, x is less than -12
so, x is set of all real numbers less than -12
e.g., x = { x | x$\in$ R , x < -12 }