Determine the inequality symbol and complete the inequality
In this exercise, we have been given the graph of a system of two linear inequalities. We will tackle them one at a time and bring them together in a system at the end.
The First Inequality
Let's take a look at the graph of the first inequality.
We can see that the boundary line is vertical and passes through ( 2,0). Therefore, the equation of the line is x= 2.
To finish forming the inequality, we need to determine the inequality symbol. This means substituting the equals sign with a blank space, since it is still unknown to us.
x ? 2
To figure out what the symbol should be, let's substitute any point that lies within the solution set into the equation.
We will substitute ( 3, 0) for this test, then make the inequality symbol fit the resulting statement.
3 is greater than 2, so the symbol will be either > or ≥. Since the boundary line in the given graph is dashed, the inequality is strict, and we can form the first inequality in the system.
x > 2
The Second Inequality
Writing the inequality for this region of the graph will involve the same steps as above.
Notice that the boundary line is vertical and passes through ( 4,0). Therefore, the equation of the line is x= 4. Once more, we substitute the equals sign with a blank space.
x ? 4
We will need another point that lies within the solution set to determine the sign of this inequality.
We will substitute ( 3, 0) for this test, then make the inequality symbol fit the resulting statement.
3 is less than 4, so the symbol will be either < or ≤. Since the boundary line in the given graph is dashed, the inequality is strict, and we can form the second inequality in the system.
x< 4
Writing the System
To complete the system of inequalities, we will bring both of our inequalities together in system notation.
x>2 x<4
