Question

solve the inequality and graph the solution.
\\( \frac{q}{-1}<2 \\)
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 left - hand side

The left - hand side \(\frac{g}{-1}\) is equal to \(-g\). So the inequality becomes \(-g<2\).

Step2: Solve for \(g\)

Multiply both sides of the inequality \(-g < 2\) by \(- 1\). When multiplying an inequality by a negative number, the direction of the inequality sign changes. So we get \(g>-2\).

To graph the solution \(g > - 2\):

• The endpoint is \(g=-2\). Since the inequality is \(>\) (not \(\geq\)), the endpoint at \(g = - 2\) is open.
• The graph is a ray starting at \(g=-2\) and extending to the right (towards positive infinity).

Answer:

The solution of the inequality is \(g>-2\). On the number - line, there is an open circle at \(-2\) and a ray extending to the right.