Question

solve the following inequation and represent your solution on the real number line -5 1/2 - x < 1/2 - 3x < 3 1/2, x € R​

Answer 1

Answer :

x € (-1 , 3)

Solution :

• Given : -5½ - x < ½ - 3x < 3½ , x € R
• To find : Solution set

We have ;

-5½ - x < ½ - 3x < 3½ , x € R

Here ,

Two cases arise ;

1) -5½ - x < ½ - 3x , x € R

AND

2) ½ - 3x < 3½ , x € R

Case1 : -5½ - x < ½ - 3x , x € R

=> -5½ - x < ½ - 3x , x € R

=> 3x - x < ½ + 5½ , x € R

=> 2x < ½ + 11⁄2 , x € R

=> 2x < (1 + 11)/2 , x € R

=> 2x < 12⁄2 , x € R

=> 2x < 6 , x € R

=> x < 6⁄2 , x € R

=> x < 3 , x € R

=> x € (-∞ , 3)

AND

Case2 : ½ - 3x < 3½ , x € R

=> ½ - 3x < 3½ , x € R

=> -3x < 3½ - ½ , x € R

=> -3x < 7⁄2 - ½ , x € R

=> -3x < (7 - 1)/2 , x € R

=> -3x < 6⁄2 , x € R

=> -3x < 3 , x € R

=> 3x > -3 , x € R

=> x > -3⁄3 , x € R

=> x > -1 , x € R

=> x € (-1 , ∞)

Here ,

The solution set of the given inequation will be given as the intersection of the solutions found in both the cases .

Thus ,

=> x € (-∞ , 3) and x € (-1 , ∞)

=> x € (-∞ , 3) ∩ (-1 , ∞)

=> x € (-1 , 3)

Hence ,

The solution set is (-1 , 3) .

Answer 2

Step-by-step explanation:

that's all I think bro wait I know it would be correct