If x = 1 - q and y = 2q + 1, then for what value of q are x and y equal (that is, x = y)?

Introduction:
This question tests solving a simple linear equation formed by equating two expressions. Since x and y are defined in terms of q, the condition “x and y are equal” means substitute the definitions and set them equal: 1 - q = 2q + 1. Then solve for q by collecting like terms. This is a direct single-step algebra problem once the equality is written correctly.

Given Data / Assumptions:

• x = 1 - q
• y = 2q + 1
• Condition: x = y
• q is a real number

Concept / Approach:
Set 1 - q equal to 2q + 1, then move all q terms to one side and constants to the other. Solve for q. Because both sides contain a constant 1, they cancel neatly, making the solution immediate.

Step-by-Step Solution:
Set x = y: 1 - q = 2q + 1 Subtract 1 from both sides: -q = 2q Add q to both sides: 0 = 3q So q = 0

Verification / Alternative check:
If q = 0, then x = 1 - 0 = 1 and y = 2*0 + 1 = 1. Since x = y, the solution is correct. If q is not 0, then -q and 2q cannot be equal, so equality fails.

Why Other Options Are Wrong:
q = 1 gives x = 0 and y = 3 (not equal). q = -1 gives x = 2 and y = -1 (not equal). q = -2 gives x = 3 and y = -3 (not equal). q = 2 gives x = -1 and y = 5 (not equal). Only 0 makes x and y match.

Common Pitfalls:
Changing signs incorrectly when moving -q, or mistakenly setting 1 - q = 2q - 1 (wrong expression for y).

Final Answer:
The value of q is 0.