Question

1 + 2v > 7
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
number line from -5 to 5 with a submit button

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( v \), we subtract 1 from both sides of the inequality \( 1 + 2v > 7 \). This gives us \( 1 + 2v - 1 > 7 - 1 \), which simplifies to \( 2v > 6 \).

Step2: Divide by 2

Next, we divide both sides of the inequality \( 2v > 6 \) by 2 to solve for \( v \). So, \( \frac{2v}{2} > \frac{6}{2} \), which simplifies to \( v > 3 \).

To graph this on the number line:

• The endpoint is at \( v = 3 \). Since the inequality is \( v > 3 \) (not \( v \geq 3 \)), we use an open circle at 3.
• The arrow points to the right (towards positive infinity) because we want all values of \( v \) greater than 3.

Answer:

The solution to the inequality \( 1 + 2v > 7 \) is \( v > 3 \). On the number line, plot an open circle at 3 and draw an arrow to the right.