to the original poster:
your error is here --
er.twi.fb wrote:let z=-5, then -15<m<-20 and suppose m=-16,so m+z=-5-16<0
"-15 < m < -20" is impossible; a number can't be both
greater than -15 and
less than -20 at once.
if this is not obvious, the obfuscation comes from the fact that the numbers are negative -- many people don't really have the proper intuition regarding negative numbers. however, the statement -15 < m < -20 is a lot like the statement 10 < m < 5; both are contradictory to themselves.
in fact, the statement 3z < m < 4z,
by itself, proves that m and z are both positive, since "3z < 4z" is a false statement unless z is positive (and once you've established that z this positive, it follows that m must also be positive, since it's sandwiched between two positive values).
Ron has been teaching various standardized tests for 20 years.
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Yves Saint-Laurent
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