N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
z+4≤9
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \( z + 4 \leq 9 \), follow these steps:

1. Isolate the variable \( z \): \[ z + 4 \leq 9 \] Subtract \( 4 \) from both sides: \[ z \leq 9 - 4 \] Simplifying gives: \[ z \leq 5 \]

2. Interpret the solution: The solution \( z \leq 5 \) means that \( z \) can be any number less than or equal to \( 5 \).

3. Graph the solution:

   • Plot the endpoint: Place a point at \( z = 5 \).
   • Select whether the endpoint is closed or open: Since the inequality is \( \leq \), use a closed dot at \( z = 5 \) to indicate that \( 5 \) is included in the solution.
   • Draw the ray: Draw a line (or ray) extending to the left from \( z = 5 \) to indicate all numbers less than \( 5 \).

4. Final representation:

   • The graph should have a closed dot at \( 5 \) and a line extending left towards negative infinity.

Here's a simple representation for visualization:

<---●========================
       5

This illustration depicts that all values to the left of \( 5 \) and including \( 5 \) itself satisfy the inequality \( z + 4 \leq 9 \).