Question

−4≤−2(y−1)<2
Step 2 of 2 : Graph the solution set.

Answer 1

draw a line between an empty point at 0 and a filled point at 3

Explanation:

To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a compound inequality and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.

We start with the original inequality:

`-4 \le -2(y-1) < 2`

From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:

`2\ge y-1 > -1`

From here we add 1 to all sides.

`3 \ge y > 0`

Although generally we would write this as:

`0 < y \le 3`

Now to graph this we would draw a hole on the number line at the point zero, and a filled point on the number line at 3, since 3 is included (since less than or equal to 3) and then just connect the two points. I'll include an image that demonstrates this.