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The Problem description is not precise, could you provide clear problem solving strategy.

Thanks.

If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1 II. 0 III. 1

A. None B. I only C. II only D. III only E. II and III

we have two equations.. 2s > 8 .. s>4, so' s' can be 4.1,5,5.05 etc and 3t < 9 .. t<3 so 't'can be 2.9999, 2,-1 etc..

if we take the lowest possible difference between s and t, we will take lowest value of s, which is just above 4 and highest value of t, which is just lower to 3.. s-t >4.0000000001 -2.999999999 .... so s-t>1 therefore all values of -1,0,1 are not possible ans none A hope it helped
_________________

I understand how we get s>4 and t<3, but I'm having a hard time wrapping my head around why t cannot be negative. Can someone please explain?

We don't need to check when t<0 but for the sake of your question, even if t <0 ---> -t>0 and you know that s>0, giving you s-t > 1 for all values of s and t as s>1

Any positive quantity added to a quantity >1 will give you the sum as >1

If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1 II. 0 III. 1

A. None B. I only C. II only D. III only E. II and III

Given: 2s > 8 Divide both sides by 2 to get: s > 4

Given: 3t < 9 Divide both sides by 3 to get: t < 3

NOTE: If we have two inequalities with the inequality symbols facing in the same direction, we can add the inequalities to learn something new.

So, take t < 3 and multiply both sides by -1 to get: -t > -3[aside: when we divide or multiply both sides of an inequality by a NEGATIVE value, we mist REVERSE the symbol]

We now have: s > 4 -t > -3

When we ADD these two inequalities, we get: s - t > 1

If s - t > 1, then: I) s - t CANNOT equal -1 II) s - t CANNOT equal 0 III) s - t CANNOT equal 1