Answer :
To solve the problem, let's examine each inequality one by one to determine for which value of [tex]\( x = q \)[/tex] the inequality holds true:
1. A. [tex]\( x + 7 > 16 \)[/tex]
- We can solve this inequality by isolating [tex]\( x \)[/tex]:
[tex]\[
x + 7 > 16 \\
x > 16 - 7 \\
x > 9
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values greater than 9.
2. B. [tex]\( x - 7 \geq 16 \)[/tex]
- Solve this inequality by isolating [tex]\( x \)[/tex]:
[tex]\[
x - 7 \geq 16 \\
x \geq 16 + 7 \\
x \geq 23
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values 23 or greater.
3. C. [tex]\( 12 - x \leq 16 \)[/tex]
- Solve this by isolating [tex]\( x \)[/tex]:
[tex]\[
12 - x \leq 16 \\
-x \leq 16 - 12 \\
-x \leq 4 \\
x \geq -4
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values greater than or equal to -4.
4. D. [tex]\( 12 + x < 16 \)[/tex]
- Solve this by isolating [tex]\( x \)[/tex]:
[tex]\[
12 + x < 16 \\
x < 16 - 12 \\
x < 4
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values less than 4.
Now we evaluate when [tex]\( x = 3 \)[/tex]:
- A: [tex]\( 3 + 7 = 10 \)[/tex], which is not greater than 16. So, False.
- B: [tex]\( 3 - 7 = -4 \)[/tex], which is not greater than or equal to 16. So, False.
- C: [tex]\( 12 - 3 = 9 \)[/tex], which is less than or equal to 16. So, True.
- D: [tex]\( 12 + 3 = 15 \)[/tex], which is less than 16. So, True.
Based on these evaluations, the inequalities [tex]\( C \)[/tex] and [tex]\( D \)[/tex] are true when [tex]\( x = 3 \)[/tex]. Therefore, the inequalities [tex]\( 12 - x \leq 16 \)[/tex] and [tex]\( 12 + x < 16 \)[/tex] are valid for [tex]\( x = 3 \)[/tex].
1. A. [tex]\( x + 7 > 16 \)[/tex]
- We can solve this inequality by isolating [tex]\( x \)[/tex]:
[tex]\[
x + 7 > 16 \\
x > 16 - 7 \\
x > 9
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values greater than 9.
2. B. [tex]\( x - 7 \geq 16 \)[/tex]
- Solve this inequality by isolating [tex]\( x \)[/tex]:
[tex]\[
x - 7 \geq 16 \\
x \geq 16 + 7 \\
x \geq 23
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values 23 or greater.
3. C. [tex]\( 12 - x \leq 16 \)[/tex]
- Solve this by isolating [tex]\( x \)[/tex]:
[tex]\[
12 - x \leq 16 \\
-x \leq 16 - 12 \\
-x \leq 4 \\
x \geq -4
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values greater than or equal to -4.
4. D. [tex]\( 12 + x < 16 \)[/tex]
- Solve this by isolating [tex]\( x \)[/tex]:
[tex]\[
12 + x < 16 \\
x < 16 - 12 \\
x < 4
\][/tex]
- This means the inequality is true for [tex]\( x \)[/tex] values less than 4.
Now we evaluate when [tex]\( x = 3 \)[/tex]:
- A: [tex]\( 3 + 7 = 10 \)[/tex], which is not greater than 16. So, False.
- B: [tex]\( 3 - 7 = -4 \)[/tex], which is not greater than or equal to 16. So, False.
- C: [tex]\( 12 - 3 = 9 \)[/tex], which is less than or equal to 16. So, True.
- D: [tex]\( 12 + 3 = 15 \)[/tex], which is less than 16. So, True.
Based on these evaluations, the inequalities [tex]\( C \)[/tex] and [tex]\( D \)[/tex] are true when [tex]\( x = 3 \)[/tex]. Therefore, the inequalities [tex]\( 12 - x \leq 16 \)[/tex] and [tex]\( 12 + x < 16 \)[/tex] are valid for [tex]\( x = 3 \)[/tex].
