Question

solve the inequality and graph the solution.
-4v - 1 ≥ 7
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( v \), we add 1 to both sides of the inequality \(-4v - 1 \geq 7\). So we get \(-4v - 1 + 1\geq7 + 1\), which simplifies to \(-4v\geq8\).

Step2: Divide by -4 (reverse inequality)

When we divide both sides of an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \(-4v\geq8\) by \(-4\), we have \(\frac{-4v}{-4}\leq\frac{8}{-4}\), which simplifies to \(v\leq - 2\).

Answer:

The solution to the inequality \(-4v - 1\geq7\) is \(v\leq - 2\). To graph this, we plot a closed circle at \(-2\) (since the inequality is "less than or equal to") and draw a ray to the left of \(-2\) (towards negative infinity).