The solution set for the inequality -4≤-2(y-1)<2 is the set of all y-values that make the inequality true.
To graph the solution set, we can begin by plotting the inequality as an inequality on the y-axis, and then identifying the solutions that make the inequality true:
First, we can simplify the left side of the inequality: -4≤-2(y-1)
Next, we can solve for y by isolating y: -4/2≤y-1
Then we can add 1 to both sides of the inequality: -2≤y
Now, we can graph the inequality y ≥ -2, which is a line that is equal to or greater than -2.
On the right side, we have -2(y-1)<2
2(y-1)>-2
y-1>-1
y>-1
So we can graph the inequality y>-1, which is a line that is greater than -1.
So the solution set is the region above the line y=-2 and below the line y=-1. The region is a strip between two lines.
It is important to note that the solution set doesn't include the values of the lines, as the inequality is strict, not inclusive.