what is the solution to the compund inequality
2
,3x-1<=5
To solve the compound inequality 2 < 3x - 1 <= 5, we need to solve two separate inequalities and combine the solutions.
First, let's solve the inequality 3x - 1 <= 5:
3x - 1 <= 5
Add 1 to both sides:
3x <= 6
Divide both sides by 3:
x <= 2
Now, let's solve the inequality 2 < 3x - 1:
2 < 3x - 1
Add 1 to both sides:
3 < 3x
Divide both sides by 3:
1 < x
Combining the solutions, the compound inequality is: 1 < x <= 2.
To solve the compound inequality 2 < 3x - 1 ≤ 5, we will break it down into two separate inequalities.
1) 2 < 3x - 1
2) 3x - 1 ≤ 5
Let's solve them step by step:
1) 2 < 3x - 1
Add 1 to both sides of the inequality:
2 + 1 < 3x - 1 + 1
3 < 3x
Divide both sides by 3:
3 / 3 < 3x / 3
1 < x
So, the first inequality is 1 < x.
2) 3x - 1 ≤ 5
Add 1 to both sides of the inequality:
3x - 1 + 1 ≤ 5 + 1
3x ≤ 6
Divide both sides by 3:
(3x) / 3 ≤ 6 / 3
x ≤ 2
So, the second inequality is x ≤ 2.
Therefore, the solution to the compound inequality 2 < 3x - 1 ≤ 5 is 1 < x ≤ 2.