Answer:
Explanation:
To solve the compound inequality -5 <= 4x - 1 < 7, we'll need to solve each inequality separately and then combine the solutions.
Starting with -5 <= 4x - 1, we'll add 1 to both sides:
-5 + 1 <= 4x - 1 + 1
-4 <= 4x
Dividing both sides by 4 (and remembering to flip the inequality since we're dividing by a positive number), we get:
-1 <= x
Now let's look at 4x - 1 < 7. We'll add 1 to both sides here too:
4x - 1 + 1 < 7 + 1
4x < 8
Dividing both sides by 4:
x < 2
So our solutions for the compound inequality are:
-1 <= x < 2
In interval notation, we write this as:
[-1, 2)