Asked by kymari davis-shanks
Solve the inequality and graph the solution.
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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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 \(-1\).
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 \(-1\).
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