First, let's split the compound inequality into two separate inequalities.
Compound Inequality:-4<gFirst Inequality:-4<gSecond Inequality: g+8<6+8+8<6
Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word
and
.
-4<g+8andg+8<6
Let's solve the inequalities separately.
First inequality
Inequalities can be solved in the same way as equations, by performing on both sides until the is isolated. The only difference is that when you divide or multiply by a negative number, you must flip the inequality sign.
This tells us that
-12 is
less than all values that satisfy the inequality.
Note that the point on -12 is open because it is not included in the solution set.
Second inequality
Once more, we will solve the inequality by isolating the variable.
This tells us that all values
less than -2 will satisfy the inequality.
Note that the point on -2 is open because it is not included in the solution set.
Compound inequality
The solution to the compound inequality is the intersection of the solution sets.
First Solution Set:-12<gSecond Solution Set: gIntersecting Solution Set: -12<g<-2<-2
Finally, we will graph the solution set to the compound inequality on a number line.