choose the correct solution and graph for the inequality (3y-6)/3 +4_<-2 or (4y-8)/2-1_>5
To find the solution for the inequality (3y-6)/3 +4 ≤ -2, we'll solve it step-by-step:
(3y-6)/3 + 4 ≤ -2
(3y-6)/3 ≤ -6
(3y-6) ≤ -18
3y ≤ -12
y ≤ -4
Now, let's find the solution for the inequality (4y-8)/2 - 1 ≥ 5:
(4y-8)/2 - 1 ≥ 5
(4y-8)/2 ≥ 6
4y-8 ≥ 12
4y ≥ 20
y ≥ 5
So, the solution to the inequality (3y-6)/3 +4 ≤ -2 is y ≤ -4, and the solution to the inequality (4y-8)/2 - 1 ≥ 5 is y ≥ 5.
The graph of the solution for y ≤ -4 would be a line or curve going from negative infinity up to and including -4 on the number line, with a shaded region below the line (representing all the values of y that satisfy the inequality).
The graph of the solution for y ≥ 5 would be a line or curve going from 5 on the number line up to positive infinity, with a shaded region above the line (representing all the values of y that satisfy the inequality).
Please note that I am unable to provide an actual graph here, but you can easily sketch it based on the descriptions provided.