SOLUTION: Given that x is GREATER than or equal to -3 and less than or equal to 7 and y is GREATER than or equal to 4 and less than or equal to 10.find the smallest possible value of x-y a

Notice that I changed two of your words "less" to "GREATER" to make more sense.
I'm pretty sure you mistook LESS THAN OR EQUAL TO (< for GREATER THAN OR
EQUAL TO >.



We want the smallest value of x-y.  We can ADD inequalities in the same order,
but we CANNOT SUBTRACT them!! So we rewrite the second one by multiplying
through by -1, which reverses the inequality symbols:



But now the inequality symbols are not in the same directions, so we can always
change the direction of an inequality by switching the largest and smallest
expressions.  So we do that with the first inequality



Now we can add them term by term:


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So the smallest possible value of x-y is -13.

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Now we'll find the smallest value of x/y.

Since there are both positive and negative numbers to form the quotient of,
and since all negative numbers are smaller than all positive numbers, the
answer must be a negative number.  The smallest possible value of x/y will be
the most negative number possible, or the negative number with the greatest
absolute
value.  That is when x=-3 any y=4.

So the smallest possible value of x/y is -3/4.

Edwin