https://file.aiquickdraw.com/mathbot/file/1726790024946gej1geni.jpg

Let's first tackle the questions in the image. I will break down the ones visible.

### 1. Writing Inequalities from Graphs (Questions 30, 32, 34):
We are asked to write the inequality based on the graph shown.

#### 30. Graph Interpretation:
The graph shows a line with an open circle at 2 and shading to the left (toward negative values). This means:
- The inequality excludes 2 and represents numbers less than 2.
- Inequality: $ x < 2 $.

#### 32. Graph Interpretation:
This graph shows a closed circle at 4 and shading to the left. A closed circle means the number 4 is included, and it represents values less than or equal to 4.
- Inequality: $ x \leq 4 $.

#### 34. Graph Interpretation:
Here, we have an open circle at -4 with shading to the right, which means it includes values greater than -4, but not -4 itself.
- Inequality: $ x > -4 $.

### 2. Solving Word Problem (Toshi Business Solutions):
The company estimates operating costs of at least $ 201,522 $ for the year and has sales of $ 98,200 $. We need to determine how much more money is required to meet the target.

This is essentially a subtraction problem:
\[ \text{Required sales} = 201,522 - 98,200 = 103,322 \]

So, Toshi Business Solutions needs at least **$103,322** more in sales to meet the target.

Would you like more details on any of these? Or clarification?

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Here are 5 additional related questions:
1. How do you graph inequalities on a number line?
2. What does an open circle versus a closed circle signify in inequalities?
3. How can you translate word problems into algebraic inequalities?
4. How do you solve multi-step inequalities?
5. How do you check your solutions for inequalities?

**Tip:** When dealing with inequalities, always remember to reverse the inequality symbol when multiplying or dividing by a negative number!

Write the inequality shown by each graph (Questions 30, 32, 34) and solve the Toshi Business Solutions word problem.

Learn how to write inequalities from number line graphs and solve business-related word problems. Includes examples such as 'x < 2', 'x ≤ 4', and how to calculate required sales to meet a target using real-world data. Suitable for Grades 7-9.

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