SOLUTION: Help me solve this equation in interval notation -1 < 3x + 5

SOLUTION: Help me solve this equation in interval notation -1 < 3x + 5 < 8.

Question 76316: Help me solve this equation in interval notation -1 < 3x + 5 < 8.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
-1 < 3x + 5 < 8
.
You need to determine the limits on just +x. You can do this by following the basic
rules of equations ... whatever you do to one section of the inequality, you must also
do to the other 2 sections of the inequality. There is, however, one exception. That
exception is that if you DIVIDE or MULTIPLY one section of the inequality by a NEGATIVE
quantity, you must do the same to all other sections AND you need to REVERSE the DIRECTION
of the inequality signs.
.
Now to this particular problem. To get closer to having just x in the middle section
of the inequality, we can eliminate the +5 by subtracting 5 from all three sections
of the inequality. When you perform that subtraction you get:
.
-6 < 3x < 3
.
Now to get just x in the middle, divide all three sections by +3 to get:
.
-2 < x < 1
.
This means that on the number line the x can be anywhere between -2 and +1.
.
That's the answer you need. Note that we did not have to apply the rule that governs
multiplying or dividing by a negative number. But remember that rule because you may
need it for other problems.
.
Hope this helps you to understand what the problem was asking you to do and how you would go
about doing it.
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