Solve the following inequalities 3 lessthan or equalto 2x92

Solve the following inequalities. 3 lessthan or equalto -2x+9/2 lessthan 7

Solution

3 < = ( -2x +9)/2 < 7

Multiplying by 2 : 6 < = ( -2x +9) < 14

Subtract -9 : -3 < = -2x < 5

Divide by 2: -3/2 < = -x < 5/2

-3/2 < = -x ----> x> = 3/2

-x < 5/2 ----> x > -5/2

So,compound solution : -5/2 < x < = 3/2