Solving the Absolute Value Puzzle: |5 - x| = 7

$|5 - x| = 7$

To solve this problem, we'll use the absolute value property, which splits the equation into two separate cases:

• Case 1: Solve $5 - x = 7$

Subtract 5 from both sides:

$5 - x - 5 = 7 - 5$

Which simplifies to:

$-x = 2$

Multiplying both sides by -1 gives:

$x = -2$

• Case 2: Solve $5 - x = -7$

Subtract 5 from both sides:

$5 - x - 5 = -7 - 5$

Which simplifies to:

$-x = -12$

Multiplying both sides by -1 gives:

$x = 12$

Thus, the solutions are $x = -2$ and $x = 12$. Now let's verify against the available choices. We can see that:

1. x = 0
2. x = -2
3. x = 12
4. Answers b + c (i.e., x = -2 and x = 12)

This confirms that the correct choice is "Answers b + c".

Therefore, the correct answer is Answers b + c.