Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

The solution set to the inequality$y\ge x$includes the$\underset{¯}{\text{boundary}}$.

Short answer

The given sentence is True.

Step-by-step solution

Step 1. Define half-plane and boundary.

When the inequality is converted into equality, equation is obtained and when the equation is graphed then the equation defines the boundary and the boundary divides the coordinate plane into two half planes.

If the boundary is included in the graph of an inequality then the solution is called closed half-plane.

If the boundary is not included in the graph of an inequality then the solution is called open half-plane.

Step 2. State whether the given sentence is true or false.

The given sentence is true because the inequality is$y\ge x$ and in the inequality, equal sign is there and therefore when the inequality is graphed, it includes the boundary therefore the solution is closed half-plane.