To determine which number from the given options satisfies the inequality [tex]\( m > \frac{7}{12} \)[/tex], we need to compare each option to [tex]\( \frac{7}{12} \)[/tex].
1. First, let’s understand what [tex]\( \frac{7}{12} \)[/tex] approximately equals to in decimal form:
[tex]\[
\frac{7}{12} \approx 0.5833
\][/tex]
2. Now, we will compare each option to [tex]\( 0.5833 \)[/tex]:
- Option a: [tex]\( -5 \)[/tex]
[tex]\[
-5 < 0.5833
\][/tex]
Clearly, [tex]\(-5\)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
- Option b: [tex]\( -9 \)[/tex]
[tex]\[
-9 < 0.5833
\][/tex]
Clearly, [tex]\(-9\)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
- Option c: [tex]\( -1 \)[/tex]
[tex]\[
-1 < 0.5833
\][/tex]
Clearly, [tex]\(-1\)[/tex] is not greater than [tex]\( \frac{7}{12} \)[/tex].
- Option d: [tex]\( 1 \)[/tex]
[tex]\[
1 > 0.5833
\][/tex]
Clearly, [tex]\( 1 \)[/tex] is greater than [tex]\( \frac{7}{12} \)[/tex].
Therefore, the number that is a solution to the inequality [tex]\( m > \frac{7}{12} \)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
