Use inverse operations on each part of the inequality.
Inequality: 1
Graph:
Practice makes perfect
In order to solve the compound inequality, we will need to isolate the x-variable in the center. To do this, we can write the compound inequality as two simple inequalities connected by an AND.
- 2 < x-3 < 5
⇕
-2 < x-3 AND x-3 < 5
We can solve each of these inequalities individually.
Next, let's graph the inequalities separately. Since x>1 can be read as "x is greater than one," we will have an open circle at one indicating that it is not a solution. The numbers that are greater than one are to its right, so this is where we will shade.
The second inequality can be read as "x is less than eight." This will have an open circle at eight. The numbers that are less than eight are to its left, so this is where we will shade on the number line.
Finally, we can graph the intersection of the two simple inequalities by combining the graphs.
The solution set for the compound inequality contains all numbers included in the shaded region. We can express this algebraically by recombining the simple inequalities.
1
