Split the compound inequality into two separate inequalities and solve them individually.
Solution: 3.75< x < 8.5 Graph:
Practice makes perfect
We are given a compound inequality.
1/4 < 2x-7/2 < 5
Let's write it as two individual inequalities. This will let us to solve each one separately.
1/4 < 2x-7/2 and 2x-7/2 < 5Now we can solve them separately and later compare their solution sets.
First inequality
We can solve inequalities just like ordinary equations. Notice that by multiplying by 2 on both sides, we can clear the fraction of the variable term and proceed to solve for x.
The second inequality is true for all values less than 8.5. Notice that x cannot equal 8.5.
Combining solution sets
Finally, we can combine the obtained solution sets. The first inequality, x>3.75, describes all values greater than 3.75, but not including 3.75. We can represent this by using an open circle at 3.75 and shading the values to the right.
The second inequality, x<8.5, describes all values less than 8.5, not including 8.5. For this, we will use an open circle again, this time at 8.5 and shade the values to the left.
The intersection of these solution sets, 3.75 < x < 8.5, describes the solutions of the compound inequality.
