What is the solution to the compound inequality?

2 < 3x – 1 ≤ 5
work out

1 answer

To solve the compound inequality, we can solve each part of the inequality separately.

First, we solve 2 < 3x - 1:
Adding 1 to both sides, we have:
2 + 1 < 3x
3 < 3x
Dividing both sides by 3, we get:
1 < x

Next, we solve 3x - 1 ≤ 5:
Adding 1 to both sides, we have:
3x - 1 + 1 ≤ 5 + 1
3x ≤ 6
Dividing both sides by 3, we get:
x ≤ 2

So the solution to the compound inequality is 1 < x ≤ 2.