Starting with the first part of the inequality:
3x - 8 ≤ 23
Add 8 to both sides to isolate 3x:
3x ≤ 23 + 8
3x ≤ 31
Now, divide both sides by 3 to solve for x:
x ≤ 31 / 3
So, the first part of the inequality gives us:
x ≤ 31/3
Now, let's solve the second part of the inequality:
-4x + 26 ≥ 6
Subtract 26 from both sides:
-4x ≥ 6 - 26
-4x ≥ -20
Divide both sides by -4. Remember that when you divide or multiply an inequality by a negative number, you need to reverse the inequality sign:
x ≤ -20 / -4
x ≤ 5
So, the second part of the inequality gives us:
x ≤ 5
Now, combining both parts, we have:
x ≤ 31/3 OR x ≤ 5
The correct choice is (Choice C):
5 ≤ x ≤ 31/3