9 - 12u + 4 + 6u > -5
Combine the 9 and the +4 as +13
Combine the -12u and the +6u as -6u
13 - 6u > -5
Subtract 13 from both sides:
13 - 6u > -5
-13 -13
-----------------
-6u > -18
Now we will divide both sides by -6,
remembering the rule:
1. If you divide both sides of an inequality by a
POSITIVE number, you DO NOT reverse the symbol
of inequality.
2. If you divide both sides of an inequality by a
NEGATIVE, number you DO reverse the symbol
of inequality.
Here we want to divide both sides of
-6u > -18
by the coefficient -6, and since -6 is NEGATIVE,
we DO reverse the symbol of inequality:
-6u/(-6) < -18/(-6)
and upon simplifying we have
u < 3
which we graph on a number line as
<======================o-------
-4 -3 -2 -1 0 1 2 3 4 5
or sometimes as
<======================)-------
-4 -3 -2 -1 0 1 2 3 4 5
and sometimes write the solution set in
set-builder notation as
{ u | u < 3 }
or in interval notation as
(-¥, 3)
Edwin
