Question 347979
Hi, 
In answer to your reply: choices being as follows for an answer to the "solution set":
a. {x|x > 2/3} b. {x|2/3 <= x <= 0} c. { } d. {x|x < 2/3}
.
Note: the results shown here indicated {{{x <= -4/3}}} and {{{x>= -2/3}}}
That is : x is to be all numbers to the left of -4/3 and all numbers to the right of -2/3.
The intersection of these graphs contains no numbers:
thus { } would be the correct response as to what is the 'solution set'
.
solving and determining the solution set are two separate steps.
The solution set of a compound inequality is always the Union of the two inequalties found to be true  or the points they have in common.  Hope this helps. 


Hi,
*Note: a step at a time

{{{3 <= 4 + 3x/2 <= 2}}}
.
Take right side:
Subtract 4 from each side
{{{3x/2 <= -2}}}
.
Multiply both sides of the two inequalities by 2/3
{{{x<= -4/3}}}
.
Take left side: Solve
{{{3 <= 4 + 3x/2}}}
{{{-1 <= 3x/2}}}
{{{-2/3 <= x}}}
.
combine
{{{-2/3 <= x<=-4/3}}}