Question 837144
<pre>
{{{matrix(1,3,7k - 1 + 2k <= 26, AND, expr(2/3)k + 8 > 12)}}}

Solve each part just like an equation:

{{{matrix(1,3,9k - 1  <= 26, AND, 3*expr(2/3)k + 3*8 > 3*12)}}}

{{{matrix(1,3,9k<= 27, AND, 2k + 24 > 36)}}}

{{{matrix(1,3,k<= 3, AND, 2k  > 12)}}}

{{{matrix(1,3,k<= 3, AND, k  > 6)}}}

The first part {{{k<=3}}} is graphed like this:

<==================]---------------------
-3 -2 -1  0  1  2  3  4  5  6  7  8  9 10

The second part {{{k>6}}} is graphed like this

----------------------------(============>
-3 -2 -1  0  1  2  3  4  5  6  7  8  9 10

These graphs have no points in common, so there is no solution.
So the solution set is empty or &#8960;.  That's because it doesn't 
make any sense to say that a value of x can be less than or 
equal to 3 AND greater than 6.  For if it's less than 3 it
CANNOT be greater than 6.  

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NOTE:

If you had been given the same inequalities with the word "OR" 
between them instead of the word "AND", then there would have been
a solution, because the word "OR" does not require any common
points.  The solution would have been:

<==================]--------(============>
-3 -2 -1  0  1  2  3  4  5  6  7  8  9 10

However it would make sense to say a value of x can be less than 
or equal 3 OR greater than 6.  But with the word "AND" between them 
the solution set is empty, because it doesn't make sense to say that 
a value of x can be less or equal to 3 AND also greater than 6.  

Edwin</pre>