What is the solution to the compound inequality?
2<3x−1≤5
(1 point)
Responses
3<x≤6
3<x≤6
1<x≤2
1<x≤2
13<x≤43
13<x≤43
1<x≤3
To solve the compound inequality 2 < 3x - 1 ≤ 5, we can break it down into two separate inequalities:
2 < 3x - 1 and 3x - 1 ≤ 5
Solving the first inequality:
2 < 3x - 1
Add 1 to both sides:
3 < 3x
Divide both sides by 3 (since we want to isolate x):
1 < x
This can also be written as x > 1
Solving the second inequality:
3x - 1 ≤ 5
Add 1 to both sides:
3x ≤ 6
Divide both sides by 3:
x ≤ 2
So, combining the two solutions, we get:
1 < x ≤ 2
Therefore, the solution to the compound inequality is 1 < x ≤ 2.
To solve the compound inequality 2 < 3x - 1 ≤ 5, we need to solve each inequality individually and then find the intersection of the solutions.
Starting with the first inequality:
2 < 3x - 1
Adding 1 to both sides, we get:
3 < 3x
Dividing both sides by 3, we have:
1 < x
Moving on to the second inequality:
3x - 1 ≤ 5
Adding 1 to both sides, we get:
3x ≤ 6
Dividing both sides by 3, we have:
x ≤ 2
Now we need to find the intersection of the solutions:
1 < x and x ≤ 2
The combined solution is 1 < x ≤ 2.