Solve the inequality and graph the solution.

Question

8y–2≤
–
10
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 \( 8y - 2 \leq -10 \), follow these steps:

1. Isolate the variable \( y \):

   Add 2 to both sides: \[ 8y - 2 + 2 \leq -10 + 2 \] Simplifying gives: \[ 8y \leq -8 \]

2. Divide by 8:

   Divide both sides by 8 (note that since 8 is positive, the inequality direction will not change): \[ y \leq -1 \]

So, the solution to the inequality is: \[ y \leq -1 \]

Graphing the Solution

1. Plot the point \( -1 \) on a number line.
2. Since the inequality is \( \leq \), use a closed circle on \( -1 \) to indicate that this value is included in the solution.
3. Draw a ray to the left of \( -1 \) to indicate that all values less than \(-1\) are also included in the solution.

This graphic representation shows that all numbers less than or equal to \(-1\) satisfy the inequality.

If you were creating the graph visually, it would look like this:

<---•=========================
     -2  -1  0  1

Here, the dot at \(-1\) is filled in, indicating that \(-1\) is included in the solution. The line continues to the left, showing all values less than \(-1\).