NDA2023MathematicsBasics of MathematicsActual
How many real numbers satisfy the equation |x-4|+|x-7|=15 ?
Options
- AOnly one
- BOnly two
- COnly three
- DInfinitely many
Correct answer
B. Only two
Step-by-step solution
|x-4|+|x-7|=15 Case 1: x 44-x+7-x=1511-2 x=152 x=-4x=-2 One solution. Case 2: 4 x 7x-4+7-x=15 No solution Case 3: x 7x-4+x-7=152 x=26x=13 One solution Total 2 solutions; x=-2,13 .