Question

solve for v and graph the solution. 3 ≤ |v - 4| click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to open circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

The absolute value inequality \( a \leq |x| \) (where \( a \geq 0 \)) is equivalent to \( x \leq -a \) or \( x \geq a \). For the inequality \( 3 \leq |v - 4| \), we can apply this rule. So we have two cases:
Case 1: \( v - 4 \leq - 3 \)
Case 2: \( v - 4 \geq 3 \)

Step2: Solve Case 1

For \( v - 4 \leq - 3 \), add 4 to both sides of the inequality.
\( v - 4+4 \leq - 3 + 4 \)
\( v \leq 1 \)

Step3: Solve Case 2

For \( v - 4 \geq 3 \), add 4 to both sides of the inequality.
\( v - 4+4 \geq 3 + 4 \)
\( v \geq 7 \)

Answer:

The solution to the inequality \( 3\leq|v - 4| \) is \( v\leq1 \) or \( v\geq7 \). To graph this, we would have a ray starting at \( 1 \) (with a filled - in circle) going to the left and a ray starting at \( 7 \) (with a filled - in circle) going to the right.