Question 150306
Find the solutions of the inequality

{{{15<3x-3(x-5)/2<=30}}}

<pre><font size = 4 color = "indigo"><b>
In a three sides inequality we solve for x in 
the middle:

Clear of fractions by multiplying all three
sides by 2:

{{{2(15)<2(3x-3(x-5)/2)  <=2(30)}}}

{{{30<2*3x-2*3(x-5)/2<=60}}}

{{{30<2*3x-cross(2)*3(x-5)/cross(2)<=60}}}

{{{30<6x-3(x-5)<=60}}}

{{{30<6x-3x+15<=60}}}

{{{30<3x+15<=60}}}

Subtract 15 for all three sides:

{{{30-15<3x+15-15<=60-15}}}

{{{15<3x<=45}}}

Divide all three sides by {{{3}}}:

{{{15/3<3x/3<=45/3}}}

{{{5<x<=15}}}

If you have had interval notation,

the interval notation is (5,15]

Edwin</pre>