Question 75680
{{{k+1/2 < k/4+2}}}
{{{4(k+1/cross(2)) < cross(4)(k/cross(4)+2)}}} Multiply both sides by 4 (this is the LCD). This clears any denominators
{{{4k+2<k+8}}}
{{{3k+2<8}}} Subtract k from both sides
{{{3k<6}}} Subtract 2 from both sides
{{{k<2}}} Divide both sides by 3. This is your solution set
If you want the answer in interval notation it is:
*[Tex \Large (-\infty,2)]
I'm not sure where you got an answer of 0 from, so double check your steps or tell me if I translated something wrong.
<p>
Check:
To test our solution set, pick any number that is less than 2 and plug it into k
{{{1+1/2 < 1/4+2}}} Let k=1
{{{2/2+1/2 < 1/4+8/4}}}
{{{3/2 < 9/4}}}
{{{3/2 < 9/4}}}
{{{1.5<2.25}}} works.