Question

Solve for x: 3 < x + 3 < 6

a 6 < x < 9
b 6 > x > 9
c 0 < x < 3
d 0 > x > 3

Answer 1

To solve the compound inequality \( 3 < x + 3 < 6 \), we can break it into two parts and solve each part separately:

1. Solve \( 3 < x + 3 \):
\[
3 - 3 < x \implies 0 < x \implies x > 0
\]

2. Solve \( x + 3 < 6 \):
\[
x < 6 - 3 \implies x < 3
\]

Now we can combine the results from the two parts:
\[
0 < x < 3
\]

Thus, the solution for \( x \) is \( 0 < x < 3 \).

Looking at the answer choices:
- a: \( 6 < x < 9 \)
- b: \( 6 > x > 9 \)
- c: \( 0 < x < 3 \) (this is correct)
- d: \( 0 > x > 3 \)

The correct answer is **c: \( 0 < x < 3 \)**.