UGCNET Questions

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.

To solve 5x + 3 = 18, we first subtract 3 from both sides to isolate the term with x. This gives 5x = 15. Dividing both sides by 5, we get x = 15 ÷ 5 = 3. Therefore, the solution of the equation is x = 3.

Option A:
Option A, 2, does not satisfy the equation because substituting x = 2 yields 5 × 2 + 3 = 13, which is not equal to 18. So this value fails to make both sides equal.

Option B:
Option B, 3, when substituted gives 5 × 3 + 3 = 15 + 3 = 18, which matches the right side and confirms that x = 3 is the correct solution.

Option C:
Option C, 4, produces 5 × 4 + 3 = 23, which is greater than 18 and so cannot be the solution.

Option D:
Option D, 5, gives 5 × 5 + 3 = 28, which again does not equal 18, and therefore cannot solve the equation.