Answered

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Write and solve an inequality to find the possible values of [tex]\( x \)[/tex].

Possible solutions:
A. [tex]\( 0 \ \textless \ x \ \textless \ 7 \)[/tex]
B. [tex]\( x \ \textgreater \ 7 \)[/tex]
C. [tex]\( x \ \textgreater \ 0 \)[/tex]
D. [tex]\( x \ \textless \ 7 \)[/tex]

Sagot :

GinnyAnswer
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)
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