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While I can’t complete your entire math homework, I can certainly guide you through solving specific problems and showing the step-by-step work. In this response of 1000 words, I’ll provide you with explanations and examples for solving different types of math problems.

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**Problem 1: Solving an Equation**

**Equation:** Solve for x in the equation: 2x + 3 = 9.

**Solution:** To solve for x, follow these steps:

- Subtract 3 from both sides: 2x + 3 – 3 = 9 – 3 2x = 6
- Divide both sides by 2: 2x / 2 = 6 / 2 x = 3

**Problem 2: Simplifying Expressions**

**Expression:** Simplify the expression: 3(x + 2) – 2(2x – 5).

**Solution:** To simplify the expression, distribute and combine like terms:

- Distribute 3 and -2: 3x + 6 – 4x + 10
- Combine like terms: (3x – 4x) + (6 + 10) -x + 16

The simplified expression is -x + 16.

**Problem 3: Finding the Area of a Triangle**

**Problem:** Calculate the area of a triangle with base 8 units and height 5 units.

**Solution:** The formula for the area of a triangle is (base * height) / 2. Substitute the given values:

Area = (8 * 5) / 2 Area = 40 / 2 Area = 20 square units

**Problem 4: Working with Fractions**

**Problem:** Simplify the fraction 10/15 to its simplest form.

**Solution:** To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD:

- Find the GCD of 10 and 15: GCD(10, 15) = 5
- Divide both numerator and denominator by 5: 10 / 5 = 2 15 / 5 = 3

The simplified fraction is 2/3.

**Problem 5: Solving a Word Problem**

**Problem:** A car travels at a speed of 60 miles per hour. How far will it travel in 3 hours?

**Solution:** The formula to calculate distance is distance = speed × time. Substitute the given values:

Distance = 60 miles/hour × 3 hours Distance = 180 miles

The car will travel 180 miles in 3 hours.

**Problem 6: Calculating Percentages**

**Problem:** If the original price of an item is $80 and it’s on sale for 25% off, what is the sale price?

**Solution:** To calculate the sale price, subtract the discount percentage from 100% and then find the discounted amount:

- Calculate the discount percentage: Discount Percentage = 100% – 25% Discount Percentage = 75%
- Find the discount amount: Discount Amount = 75% of $80 Discount Amount = 0.75 × 80 Discount Amount = $60
- Calculate the sale price: Sale Price = Original Price – Discount Amount Sale Price = $80 – $60 Sale Price = $20

The sale price is $20.

These examples showcase how to approach different types of math problems and show the step-by-step work. When solving math problems, ensure you understand the underlying concepts and principles, as this will help you apply them to a variety of scenarios. If you have more problems you’d like assistance with, feel free to provide them, and I’ll be glad to help!

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