Question

Solve |x - 3| > 8.

a) x
b) x > 5 or x < -3
c) x > 24 or x < -11
d) x

Answer 1

The solution to the inequality |x - 3| > 8 is the set of all x that either satisfy x > 11 or satisfy x < -5, which is represented as x.

Step-by-step explanation:

The student has asked to solve the inequality |x - 3| > 8. To solve for x, we approach the absolute value inequality as two separate cases:

1. x - 3 > 8, which simplifies to x > 11.
2. -(x - 3) > 8, which is the same as -x + 3 > 8. Solving for x in this scenario gives us x < -5.

Therefore, the solution to the inequality is the set of all x that satisfy either condition, represented by the answer x.

This matches option (a) among the choices provided by the student.