SOLUTION: -4<-3x-13<26

Question 72905: -4<-3x-13<26
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
-4<-3x-13<26
.
Add 13 to all three sections of this inequality to get:
.
-4 + 13 < -3x - 13 + 13 < 26 + 13
.
This simplifies to
.
+9 < -3x < 39
.
Divide all three sections by -3 and you get:
.
-3 < x < -13
.
BUT a rule of inequalities is that if you multiply or divide by a negative number, the inequality
arrows flip around in the other direction. Don't forget this rule! And since we divided by
negative 3 we have to flip the arrows to get:
.
-3 > x > -13
.
This says that on the number line x lies between -3 and -13.
.
Let's pick a number in this domain and substitute it into the original problem to make
sure that it works. -10 is an easy number to choose and it is between -3 and -13.
.
The original problem was:
.
-4<-3x-13<26
.
Substituting -10 for x we get
.
-4 < 30-13 < 26
.
And solving the middle section results in:
.
-4 < +17 < +26
.
That's correct ... + 17 lies between -4 and + 26. That adds a little "comfort factor" that
our answer is correct.
.
Hope this helps you to understand inequalities a little better.
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