Problem: m/5-3˃3/5-m/2
Answer in integer or a fraction.
m/5 - 3 ˃ 3/5 - m/2
m/5 - 3 + 3 ˃ 3/5 - m/2 + 3
m/5 ˃ 3 3/5 - m/2
m/5 + m/2 ˃ 3 3/5 - m/2 + m/2
m/5 + m/2 ˃ 3 3/5
m/5 + m/2 ˃ 18/5
m/5 + m/2 ˃ 18/5
10 * (m/5 + m/2) ˃ 18/5 * 10
2m + 5m ˃ 18/5 * 10
7m ˃ 18 * 2
7m > 36
m > 36/7
m > 5 1/7
We can check the answer by putting some
value for m into the inequatlity. What
we can't do is use 5 1/7; that would give
the same value on both sides, which is not
an inequality. We must choose any number
that is larger than 5 1/7. Try a few.
m/5 - 3 ˃ 3/5 - m/2
10/5 - 3 ˃ 3/5 - 10/2
2 - 3 > 3/5 - 5
-1 > -4.4
m/5 - 3 ˃ 3/5 - m/2
20/5 - 3 ˃ 3/5 - 20/2
4 - 3 > 3/5 - 10
1 > -9.4
m/5 - 3 ˃ 3/5 - m/2
6/5 - 3 ˃ 3/5 - 6/2
1.2 - 3 > 0.6 - 3
-1.8 > -2.4
It checks.
Answer: m > 5 1/7