Solve the linear equation 5x - 40 = 3x and then find the numerical value of the expression 2x - 11.

Introduction / Context:
This is a straightforward linear equation problem followed by an evaluation of a simple expression in x. Such questions test your basic algebraic manipulation skills: isolating x and then substituting the value into another expression. Although simple, they appear frequently in the arithmetic and algebra sections of aptitude tests and must be done quickly and accurately.

Given Data / Assumptions:

• The equation is 5x - 40 = 3x.
• x is a real number.
• We are asked to find the value of 2x - 11 after solving for x.

Concept / Approach:
We solve the equation 5x - 40 = 3x by bringing all x terms to one side and constants to the other. Once we obtain the value of x, we directly substitute it into 2x - 11. There is no need for any advanced technique; the main focus is on careful and correct algebraic manipulation.

Step-by-Step Solution:
Start with the equation: 5x - 40 = 3x. Subtract 3x from both sides to collect x terms: 5x - 3x - 40 = 0. This simplifies to 2x - 40 = 0. Add 40 to both sides: 2x = 40. Divide by 2: x = 40 / 2 = 20. Now evaluate the expression 2x - 11. Substitute x = 20: 2x - 11 = 2 * 20 - 11. Compute 2 * 20 = 40. So 2x - 11 = 40 - 11 = 29.

Verification / Alternative check:
We can verify x = 20 satisfies the original equation. Substitute into 5x - 40: 5 * 20 - 40 = 100 - 40 = 60. Substitute into 3x: 3 * 20 = 60. The two sides are equal, confirming that x = 20 is correct. With x confirmed, the calculation 2x - 11 = 40 - 11 = 29 is reliable.

Why Other Options Are Wrong:
If you misplaced a sign or made an arithmetic mistake, you might get 19, 9, or even 39. For example, forgetting to add 40 correctly or miscomputing 2 * 20 could lead to these errors. The value 0 would arise only if 2x - 11 were mistakenly set equal to the equation itself instead of being evaluated after solving. None of these incorrect values satisfy both the equation and the expression simultaneously.

Common Pitfalls:
A frequent error is to subtract 5x from both sides and write 3x - 5x - 40 = 0 incorrectly, leading to -2x - 40 = 0 and then mistakes with signs. Another pitfall is to forget that you must substitute the solved value of x into 2x - 11, not into the original equation again. Careful stepwise operations prevent these issues.

Final Answer:
The numerical value of 2x - 11 is 29.