Let's solve the inequality [tex]\( m > \frac{7}{12} \)[/tex] and determine which number from the given options satisfies this inequality.
The inequality we need to check is [tex]\( m > \frac{7}{12} \)[/tex].
Given options are:
a) [tex]\( -5 \)[/tex]
b) [tex]\( -9 \)[/tex]
c) [tex]\( -1 \)[/tex]
d) [tex]\( 7 \)[/tex]
We'll compare each option to [tex]\( \frac{7}{12} \)[/tex] to see if it satisfies the inequality.
1. Option a: [tex]\( -5 \)[/tex]
We need to check if [tex]\( -5 > \frac{7}{12} \)[/tex].
- Comparing: [tex]\( -5 \)[/tex] is much less than [tex]\( \frac{7}{12} \)[/tex].
- Result: [tex]\( -5 \)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
2. Option b: [tex]\( -9 \)[/tex]
We need to check if [tex]\( -9 > \frac{7}{12} \)[/tex].
- Comparing: [tex]\( -9 \)[/tex] is much less than [tex]\( \frac{7}{12} \)[/tex].
- Result: [tex]\( -9 \)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
3. Option c: [tex]\( -1 \)[/tex]
We need to check if [tex]\( -1 > \frac{7}{12} \)[/tex].
- Comparing: [tex]\( -1 \)[/tex] is less than [tex]\( \frac{7}{12} \)[/tex].
- Result: [tex]\( -1 \)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
4. Option d: [tex]\( 7 \)[/tex]
We need to check if [tex]\( 7 > \frac{7}{12} \)[/tex].
- Comparing: [tex]\( 7 \)[/tex] is much greater than [tex]\( \frac{7}{12} \)[/tex].
- Result: [tex]\( 7 \)[/tex] is greater than [tex]\( \frac{7}{12} \)[/tex].
So, the number from the given options that is a solution to the inequality [tex]\( m > \frac{7}{12} \)[/tex] is [tex]\( 7 \)[/tex].
Thus, the correct answer is:
d) [tex]\( 7 \)[/tex]
