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Answer :
Let's evaluate each inequality step-by-step when [tex]\( x = 9 \)[/tex] and determine which one is true:
A. [tex]\( x + 7 > 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 9 + 7 > 16 \][/tex]
This simplifies to:
[tex]\[ 16 > 16 \][/tex]
This statement is not true, as 16 is not greater than 16. Therefore, option A is false.
B. [tex]\( x - 7 \geq 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 9 - 7 \geq 16 \][/tex]
This simplifies to:
[tex]\[ 2 \geq 16 \][/tex]
This statement is not true, as 2 is not greater than or equal to 16. Therefore, option B is false.
C. [tex]\( 12 - x \leq 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 12 - 9 \leq 16 \][/tex]
This simplifies to:
[tex]\[ 3 \leq 16 \][/tex]
This statement is true, as 3 is indeed less than or equal to 16. Therefore, option C is true.
D. [tex]\( 12 + x < 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 12 + 9 < 16 \][/tex]
This simplifies to:
[tex]\[ 21 < 16 \][/tex]
This statement is not true, as 21 is not less than 16. Therefore, option D is false.
From this analysis, the only inequality that is true when [tex]\( x = 9 \)[/tex] is option C: [tex]\( 12 - x \leq 16 \)[/tex].
A. [tex]\( x + 7 > 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 9 + 7 > 16 \][/tex]
This simplifies to:
[tex]\[ 16 > 16 \][/tex]
This statement is not true, as 16 is not greater than 16. Therefore, option A is false.
B. [tex]\( x - 7 \geq 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 9 - 7 \geq 16 \][/tex]
This simplifies to:
[tex]\[ 2 \geq 16 \][/tex]
This statement is not true, as 2 is not greater than or equal to 16. Therefore, option B is false.
C. [tex]\( 12 - x \leq 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 12 - 9 \leq 16 \][/tex]
This simplifies to:
[tex]\[ 3 \leq 16 \][/tex]
This statement is true, as 3 is indeed less than or equal to 16. Therefore, option C is true.
D. [tex]\( 12 + x < 16 \)[/tex]
Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 12 + 9 < 16 \][/tex]
This simplifies to:
[tex]\[ 21 < 16 \][/tex]
This statement is not true, as 21 is not less than 16. Therefore, option D is false.
From this analysis, the only inequality that is true when [tex]\( x = 9 \)[/tex] is option C: [tex]\( 12 - x \leq 16 \)[/tex].
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