Question 18

x = 2

To solve the equation \((2x-3)/5 = x/10\), we can multiply both sides by 10 to eliminate the denominators, leading to \(4x - 6 = x\). This simplifies to \(3x = 6\), resulting in \(x = 2\).

A) 2

This option is correct because substituting \(x = 2\) back into the original equation, we have \((2(2)-3)/5 = 2/10\) which simplifies to \(1/5 = 1/5\), confirming that \(x = 2\) is indeed a solution.

B) 3

This option is incorrect as substituting \(x = 3\) into the equation results in \((2(3)-3)/5 = 3/10\) which simplifies to \(3/5 = 3/10\), a false statement. Therefore, \(x = 3\) does not satisfy the equation.

C) 15

This option is also incorrect. Substituting \(x = 15\) gives \((2(15)-3)/5 = 15/10\), simplifying to \(27/5 = 3/2\), which is not true. Hence, \(x = 15\) does not solve the equation.

D) 10

This option is incorrect as well. Plugging \(x = 10\) into the equation results in \((2(10)-3)/5 = 10/10\), which simplifies to \(17/5 = 1\), an incorrect statement. Thus, \(x = 10\) is not a solution.

Conclusion

The only viable solution to the equation \((2x-3)/5 = x/10\) is \(x = 2\), as confirmed by substituting it back into the equation. All other options do not satisfy the equation, demonstrating that they are incorrect. Therefore, \(A) 2\) is definitively the correct answer.