N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
y–8≤1
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 \( y - 8 \leq 1 \), we first isolate \( y \).

1. Add 8 to both sides: \[ y - 8 + 8 \leq 1 + 8 \] \[ y \leq 9 \]

Now we have the inequality \( y \leq 9 \).

Graphing the solution:

1. Plot the endpoint:

   • Plot the point \( (9, y) \) on the y-axis.

2. Choose the endpoint type:

   • Since the inequality is \( \leq \) (less than or equal to), we use a closed dot (●) at \( y = 9 \) to indicate that \( 9 \) is included in the solution.

3. Draw the ray:

   • From the closed dot at \( y = 9 \), draw a ray extending to the left (downward for the y-axis) to indicate that \( y \) can take any value less than or equal to \( 9 \).

Summary of the solution:

The solution to the inequality \( y - 8 \leq 1 \) is \( y \leq 9 \), represented graphically with a closed dot at \( 9 \) and a ray extending to the left.