Question

What are the solutions for the absolute value equation ∣5−x∣=6?

a.x=−1,11
b.x=−1,11
c.x=−11,1
d.x=−11,1

Answer 1

The absolute value equation |5−x| = 6 has two solutions, x = -1 and x = 11. The solutions result from considering that the expression inside the absolute value can be both positive and negative.

Step-by-step explanation:

The absolute value equation |5−x| = 6 has two solutions because absolute value expressions can be equal to the positive or negative of the number on the other side of the equation. To solve, consider both cases:

1. If 5 − x is positive, then 5 − x = 6. Solving for x, x = 5 − 6, so x = -1.
2. If 5 − x is negative, then 5 − x = -6. Solving for x, x = 5 + 6, so x = 11.

Therefore, the solutions for the equation are x = −1 and x = 11.