Sure! Let's find the possible values of [tex]\( x \)[/tex] given the inequality options. We'll analyze each option step by step to determine which one correctly represents the given inequality [tex]\( 0 < x < 7 \)[/tex].
### Step-by-Step Analysis:
#### Option 1: [tex]\( 0 < x < 7 \)[/tex]
- This option indicates that [tex]\( x \)[/tex] must be greater than 0 and less than 7. This precisely matches the given inequality [tex]\( 0 < x < 7 \)[/tex].
- Therefore, this option is a correct representation of the inequality.
#### Option 2: [tex]\( x > 7 \)[/tex]
- This option indicates that [tex]\( x \)[/tex] must be greater than 7. It does not match the given inequality [tex]\( 0 < x < 7 \)[/tex], as it excludes all values between 0 and 7.
- Therefore, this option is not a correct representation of the inequality.
#### Option 3: [tex]\( x > 0 \)[/tex]
- This option indicates that [tex]\( x \)[/tex] must be greater than 0. While this is true for the given inequality [tex]\( 0 < x < 7 \)[/tex], it does not restrict [tex]\( x \)[/tex] to be less than 7. It allows [tex]\( x \)[/tex] to be any positive number, which is not the same as the given inequality.
- Therefore, this option is not a correct representation of the inequality.
#### Option 4: [tex]\( x < 7 \)[/tex]
- This option indicates that [tex]\( x \)[/tex] must be less than 7. While this is true for the given inequality [tex]\( 0 < x < 7 \)[/tex], it does not restrict [tex]\( x \)[/tex] to be greater than 0. It allows [tex]\( x \)[/tex] to be any number less than 7, including negative numbers and zero, which is not the same as the given inequality.
- Therefore, this option is not a correct representation of the inequality.
### Conclusion:
After analyzing all the options, the only option that correctly represents the given inequality [tex]\( 0 < x < 7 \)[/tex] is:
[tex]\[ \boxed{0 < x < 7} \][/tex] (Option 1)
