Question

solve the inequality and graph the solution.
\\( \frac { j } { - 1 } \geq 4 \\)
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.

Explanation:

Step1: Simplify the inequality

Multiply both sides of the inequality \(\frac{j}{-1}\geq4\) by \(- 1\). Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes. So we have \(j\leq - 4\).

Step2: Graph the solution

On the number - line:

• The endpoint is at \(j = - 4\). Since the inequality is \(j\leq - 4\), the endpoint is a closed circle (because the value \(j=-4\) is included in the solution set).
• The graph is a ray that extends to the left (towards more negative values) from \(j = - 4\).

Answer:

The solution of the inequality is \(j\leq - 4\). On the number - line, there is a closed circle at \(-4\) and a ray extending to the left.