UGC NET Questions (Paper – 1)

To solve 3x − 5 = 2x + 7, we first bring like terms together. Subtracting 2x from both sides gives x − 5 = 7. Then we add 5 to both sides to isolate x, obtaining x = 12. This value satisfies the equation when substituted back, confirming that 12 is the correct solution.

Option A:
Option A, 6, does not satisfy the equation because substituting x = 6 gives 3 × 6 − 5 = 13 and 2 × 6 + 7 = 19, which are not equal. This indicates that 6 cannot be the solution.

Option B:
Option B, 10, also fails on substitution, as 3 × 10 − 5 equals 25 while 2 × 10 + 7 equals 27, showing a mismatch between the two sides.

Option C:
Option C results in equal values on both sides when substituted, with 3 × 12 − 5 giving 31 and 2 × 12 + 7 also giving 31. This equality verifies that x = 12 satisfies the original equation.

Option D:
Option D, 15, leads to 3 × 15 − 5 = 40 and 2 × 15 + 7 = 37, again producing unequal sides and ruling out 15 as a solution.