What is the solution to the compound inequality?
2 < 3x – 1 ≤ 5
To solve the compound inequality, we'll solve each inequality separately and then find the intersection of the solutions.
For the first inequality, 2 < 3x - 1, we'll add 1 to both sides:
2 + 1 < 3x
3 < 3x
Divide both sides by 3:
1 < x
For the second inequality, 3x - 1 ≤ 5, we'll add 1 to both sides:
3x - 1 + 1 ≤ 5 + 1
3x ≤ 6
Divide both sides by 3:
x ≤ 2
The solution to the compound inequality is:
1 < x ≤ 2