Solve the compound inequality.
-3 < 2x - 3 < 5
-3 < 2x - 3 < 5
0 < 2x < 8
0 < x < 4
To solve the compound inequality -3 < 2x - 3 < 5, we need to break it down into two separate inequalities and solve each one individually.
First, let's focus on the left inequality:
-3 < 2x - 3
Adding 3 to both sides, we get:
0 < 2x
Dividing both sides by 2, we have:
0/2 < 2x/2
0 < x
So the solution to the left inequality is x > 0.
Now, let's turn our attention to the right inequality:
2x - 3 < 5
Adding 3 to both sides, we get:
2x < 8
Dividing both sides by 2, we have:
2x/2 < 8/2
x < 4
Therefore, the solution to the right inequality is x < 4.
Combining the solutions to both inequalities, we have:
0 < x < 4
So the compound inequality -3 < 2x - 3 < 5 is solved for x as 0 < x < 4.
To solve the compound inequality -3 < 2x - 3 < 5, we need to isolate the variable x.
Let's start by adding 3 to all parts of the inequality:
-3 + 3 < 2x - 3 + 3 < 5 + 3
0 < 2x < 8
Next, we divide all parts of the inequality by 2 to solve for x:
0/2 < 2x/2 < 8/2
0 < x < 4
Therefore, the solution to the compound inequality -3 < 2x - 3 < 5 is 0 < x < 4.