If 4x - 5 = 3x - 1, then what is the numerical value of (x + 4)^2?

Introduction / Context:
This question checks your understanding of solving a simple linear equation in one variable and then using that solution to evaluate a related expression. It is a classic aptitude style problem where you first determine the value of x and then substitute this value into (x + 4)^2 to get a numerical result.

Given Data / Assumptions:

• The equation 4x - 5 = 3x - 1 is given.
• We need to find the numerical value of (x + 4)^2.
• x is a real number and normal arithmetic rules apply.

Concept / Approach:
The approach is to first isolate x by collecting all x terms on one side of the equation and constants on the other. Once x is known, you substitute it into (x + 4)^2 and simplify using basic algebra. Squaring a binomial means multiplying the same bracket by itself and computing the result.

Step-by-Step Solution:

Verification / Alternative check:
You can verify by substituting x = 4 back into the original equation. Left-hand side: 4*4 - 5 = 16 - 5 = 11. Right-hand side: 3*4 - 1 = 12 - 1 = 11. Since both sides are equal, x = 4 is correct. The computed value of (x + 4)^2 = 64 is therefore reliable.

Why Other Options Are Wrong:

Common Pitfalls:
Students sometimes forget that (x + 4)^2 means (x + 4) multiplied by itself and not simply doubling x + 4. Another frequent mistake is mismanaging signs when moving terms across the equality sign. Carefully isolating x and then squaring only after substitution avoids these errors.

Final Answer:
64