Choose the correct solution and graph for the inequality.
(3y-6)/3 + 4 less than or equal to -2 or (4y-8)/2- 1 greater than or eual to 5
To solve the inequality, we will work on each part separately.
First, let's solve the inequality (3y-6)/3 + 4 ≤ -2:
(3y-6)/3 + 4 ≤ -2
(3y-6)/3 ≤ -2 - 4
(3y-6)/3 ≤ -6
(3y-6) ≤ -6 * 3
3y - 6 ≤ -18
3y ≤ -18 + 6
3y ≤ -12
y ≤ -12/3
y ≤ -4
Now, let's solve the inequality (4y-8)/2 - 1 ≥ 5:
(4y-8)/2 - 1 ≥ 5
(4y-8)/2 ≥ 5 + 1
(4y-8)/2 ≥ 6
4y - 8 ≥ 6 * 2
4y - 8 ≥ 12
4y ≥ 12 + 8
4y ≥ 20
y ≥ 20/4
y ≥ 5
Now we have two inequalities:
y ≤ -4
y ≥ 5
Graphically, the solution is the intersection of both solutions, which gives a solution of y ≥ 5 (since no values of y can satisfy both inequalities).
Graph:
```
------------- ◉◉◉◉◉ ◉◉◉◉◉ -------------
y <---|---|-4 infinity
-4 <--- y --->
-------------------------->
```
Solution: y ≥ 5