Question

Solve the inequality: |x-5| < 7

Options:
a) x < -2 or x > 12
b) x < -12 or x > 2
c) -2 < x < 12
d) -12 < x < 2

Answer 1

(c)

Step-by-step explanation:

given the inequality

| x - 5 | < 7

inequalities of the type | x | < a, have solutions in the form

- a < x < a

Then

- 7 < x - 5 < 7 ( add 5 to each interval )

- 2 < x < 12

Answer 2

To solve the inequality |x-5| < 7, we consider two cases and find that the solution is -2 < x < 12.

Step-by-step explanation:

To solve the inequality |x-5| < 7, we need to consider two cases:

1. If x-5 is positive, then the inequality becomes x-5 < 7. Solving this inequality gives x < 12.
2. If x-5 is negative, then the inequality becomes -(x-5) < 7. Simplifying gives -x+5 < 7. Solving this inequality gives x > -2.

Combining the two cases, we have -2 < x < 12. Therefore, the correct option is c) -2 < x < 12.