Question 38553: solve the inequality symbolically. Express the solution set in interval notation.
7y-2<-6y-7
Found 2 solutions by fractalier, AnlytcPhil:
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! From
7y - 2 < -6y - 7
we add 6y to both sides
13y - 2 < -7
now add 2 to both sides
13y < -5
y < -5/13
The solution is {y : y < -5/13}
It has been pointed out to me, correctly, that the proper notation is
(infinity, -5/13)
Answer by AnlytcPhil(1810)  (Show Source):
You can put this solution on YOUR website! Solve the inequality symbolically. Express the solution set in interval
notation.
7y - 2 < -6y - 7
Solve it just as you would an equation
Get rid of the -2 on the left by adding +2 to both sides
7y - 2 < -6y - 7
+ 2 + 2
——————————————————
7y < -6y - 5
Get rid of the -6y on the right by adding +6y to both sides
7y < -6y - 5
+6y +6y
———————————————
13y < -5
Divide both sides by 13. Note: if you were dividing by a
negative number, you would reverse the inequality symbol;
however here we are dividing by a positive number 13, so
we DO NOT reverse the inequality symbol:
13y < -5
y < -5/13
Now draw a number line, and mark -5/13 approximately
which is between -1 and 0, closer to 0
--------------o-----------
-2 -1 0 1
Since y is less than -5/13, shade the left side of -5/13
<==============o-----------
-2 -1 0 1
We imagine that there is a -¥ on the far
left of the number line and an ¥ on the
far right side
-¥ <==============o----------- ¥
-2 -1 0 1
The left "endpoint" of the shaded region is -¥ and the
right endpoint is -5/13, so the interval notation has these
two endpoints. Neither endpoint is included, so the interval
notation has ( ) of each side, not [ ]:
Interval notation of solution: (-¥,-5/13)
Edwin McCravy
AnlytcPhil@aol.com
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