Split the compound inequality into two separate inequalities.
Solution Set: -4Graph:
Practice makes perfect
First, let's split the compound inequality into separate inequalities.
Compound Inequality: -10< 3x&+ 2 ≤ 8
First Inequality: -10< 3x&+2
Second Inequality: 3x &+2 ≤ 8
Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word "and."
-10< 3x+2 and 3x+2 ≤ 8
Let's solve the inequalities separately.
First inequality
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must flip the inequality sign.
This inequality tells us that all values less than or equal to 2 will satisfy the inequality.
Note that the point on 2 is closed because it is included in the solution set.
Compound inequality
The solution to the compound inequality is the intersection of the solution sets.
First Solution Set: - 4< x&
Second Solution Set: x&≤ 2
Intersecting Solution Set: - 4< x& ≤ 2
Finally, we will graph the solution set to the compound inequality on a number line.
