SOLUTION: I am really stumped as to how to solve this inequality. I would appreciate ANY answers. I just, for some reason, cannot work this one. 3a + 8/2

SOLUTION: I am really stumped as to how to solve this inequality. I would appreciate ANY answers. I just, for some reason, cannot work this one. 3a + 8/2 < 10 Thanks so much. :)

Question 80895This question is from textbook Glenco Mathematics Algebra 1
: I am really stumped as to how to solve this inequality.
I would appreciate ANY answers. I just, for some reason, cannot work this one.
3a + 8/2 < 10
Thanks so much. :) This question is from textbook Glenco Mathematics Algebra 1

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You can work problems of this type just as you would solve an equation with the exception that
if you divide or multiply by a negative quantity, then you must reverse the direction
of the inequality sign.
.
So let's start with the given expression:
.

.
Notice that so we can replace it by 4 to get:
.

.
Get rid of the 4 on the left side by subtracting 4 from both sides of the inequality
to get:
.

.
Now reduce the left side to just "+a" by dividing both sides of the inequality by +3
to get:
.

.
which simplifies to
.
The original inequality should be satisfied as long as the value of "a" is less than 2.
.
Let's build our self confidence by trying some values for "a". Suppose we let "a" equal
zero. That value is obviously less than +2. If we substitute zero for a in the original
inequality we get:
.
which becomes . That works. Similarly, if we let a = +1
the original inequality becomes:
.
and this further simplifies to . That works also.
.
Now let's set a = +3. That is outside the limit we found since +3 is not less than +2.
.
With a = +3 the original inequality becomes:
.
. This simplifies to , and this obviously is not true.
.
From these spot checks, it seems as though our answer is correct.
.
Hope this helps you to understand the problem.
.
Cheers.
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