Question

|2v|< 2
This must be marked on a
number line

Answer 1

Answer: I understand that you want to solve the inequality |2v|< 2 and mark the solution on a number line. Here are the steps to do that:

First, we need to find the values of v that make the absolute value expression less than 2. We can do this by splitting the inequality into two cases: when 2v is positive and when 2v is negative.

If 2v is positive, then |2v| = 2v, and we can solve the inequality by dividing both sides by 2: 2v < 2 => v < 1. This means that any value of v that is less than 1 will satisfy the inequality.

If 2v is negative, then |2v| = -2v, and we can solve the inequality by dividing both sides by -2 and reversing the direction of the inequality sign: -2v < 2 => v > -1. This means that any value of v that is greater than -1 will satisfy the inequality.

Combining these two cases, we get that the solution set for v is -1 < v < 1. This means that any value of v that is between -1 and 1 (not including -1 and 1) will satisfy the inequality.

To mark this solution on a number line, we can use parentheses to indicate that the endpoints are not included, and draw a line segment between them to show the range of values. The number line will look like this:

![number line]

Answer 2

1. 2. When 2v is negative:
2. - Multiply both sides of the inequality by -1: |-2v| < 2
3. - This simplifies to |2v| < 2, which is the same inequality as before.
4. - Since the inequality remains the same, the solution for this case is the same as the first case.
5. - Mark a filled circle at -1 and 1 on the number line, and draw a line segment connecting them. Shade the region between -1 and 1, but do not include -1 and 1.
7. Combining the two cases, the solution for the inequality |2v| < 2 is the region between -1 and 1, excluding -1 and 1.

Explanation:

To mark the inequality |2v| < 2 on a number line, we need to consider two cases: when 2v is positive and when 2v is negative.

1. When 2v is positive:

- Divide both sides of the inequality by 2: |v| < 1

- This means that v is any number between -1 and 1, excluding -1 and 1.

- Mark a filled circle at -1 and 1 on the number line, and draw a line segment connecting them. Shade the region between -1 and 1, but do not include -1 and 1.

1. 2. When 2v is negative:
2. - Multiply both sides of the inequality by -1: |-2v| < 2
3. - This simplifies to |2v| < 2, which is the same inequality as before.
4. - Since the inequality remains the same, the solution for this case is the same as the first case.
5. - Mark a filled circle at -1 and 1 on the number line, and draw a line segment connecting them. Shade the region between -1 and 1, but do not include -1 and 1.
7. Combining the two cases, the solution for the inequality |2v| < 2 is the region between -1 and 1, excluding -1 and 1.