COMEDK202510 May 2025Morning ShiftMathematicsBasics of MathematicsActual
The solution set of the system of inequalities 5-4 x -7 or 5-4 x 7, x R is
Options
- A(- ,- 1 2 ) (3, )
- B(- ,- 1 2 ] [3, )
- C(- ,- 1 2 ] (3, )
- D(- ,- 1 2 ) [3, )
Correct answer
B. (- ,- 1 2 ] [3, )
Step-by-step solution
The given system of inequalities is 5 - 4x -7 or 5 - 4x 7 . Solving the first inequality: 5 - 4x -7 -4x -7 - 5 -4x -12 Dividing by -4 reverses the inequality sign: x -12 -4 x 3 Solving the second inequality: 5 - 4x 7 -4x 7 - 5 -4x 2 Dividing by -4 reverses the inequality sign: x 2 -4 x - 1 2 The solution set is the union of these two intervals: x (- , - 1 2 ] [3, ) Answer: (- ,- 1 2 ] [3, )