High School

1. Which inequality is true when [tex]$x=9$[/tex]?

A. [tex]$x+7\ \textgreater \ 16$[/tex]
B. [tex][tex]$x-7 \geq 16$[/tex][/tex]
C. [tex]$12-x \leq 16$[/tex]
D. [tex]$12+x\ \textless \ 16$[/tex]

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].