Solve the inequality.

−7h−8≤3h−7

Show your work. Make sure to graph your solution on the number line provided.

To solve the inequality \(-7h - 8 \leq 3h - 7\), we will follow these steps:

### Step 1: Isolate the variable
First, we want to get all terms involving \(h\) on one side and the constant terms on the other side.

1. Add \(7h\) to both sides:
   \[
   -8 \leq 3h + 7h - 7
   \]
   This simplifies to:
   \[
   -8 \leq 10h - 7
   \]

2. Next, add \(7\) to both sides:
   \[
   -8 + 7 \leq 10h
   \]
   This simplifies to:
   \[
   -1 \leq 10h
   \]

### Step 2: Solve for \(h\)
Now, divide both sides by \(10\):
\[
-\frac{1}{10} \leq h
\]
This can be rewritten as:
\[
h \geq -\frac{1}{10}
\]

### Step 3: Graph the solution
On a number line, this inequality means that \(h\) is greater than or equal to \(-\frac{1}{10}\). We represent this with a solid dot at \(-\frac{1}{10}\) and a line extending to the right.

### Graph
To visualize:

```
<---o================>
    -1/10
```

### Conclusion
The solution to the inequality is:
\[
h \geq -\frac{1}{10}
\]

Do you want more details or have any questions? Here are some related questions to consider:

1. What are the steps to solve a linear equation?
2. How do you represent inequalities on a number line?
3. Can you give an example of a different linear inequality?
4. What happens to the inequality sign if you multiply or divide by a negative number?
5. How would you solve a system of inequalities?

**Tip:** Always check your solution by substituting back into the original inequality!

Explore how to solve the linear inequality -7h - 8 ≤ 3h - 7 with a step-by-step approach, including isolating the variable and graphing the solution on a number line. Understand core concepts like algebraic manipulation, inequality properties, and visual representation for students in Grades 7-9.

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