There are 8 more male students than females in a college level math class. This total number of students in the class is 26. Find the number of male and female students. Clear parenthesis and combine like terms. 
−2(𝑥𝑥−4) −3(𝑥𝑥+2𝑦𝑦) 
Show all the work.

To solve the problem of finding the number of male and female students in the class, we can set up a system of equations.

### Step 1: Defining variables
Let:
- \( x \) be the number of female students in the class.
- \( x + 8 \) be the number of male students, since there are 8 more males than females.

### Step 2: Setting up an equation
The total number of students is 26. So, we can write the equation:
\[
x + (x + 8) = 26
\]

### Step 3: Simplifying the equation
Now, combine like terms:
\[
x + x + 8 = 26
\]
\[
2x + 8 = 26
\]

### Step 4: Solving for \( x \)
Subtract 8 from both sides:
\[
2x = 18
\]
Now, divide both sides by 2:
\[
x = 9
\]
So, there are 9 female students.

### Step 5: Finding the number of male students
Since there are 8 more male students than female students, the number of male students is:
\[
9 + 8 = 17
\]

### Final Answer:
- Number of female students = 9
- Number of male students = 17

### Now, solving the expression \( −2(x−4) −3(x+2y) \)

### Step 1: Distribute
Distribute the terms:
\[
-2(x - 4) = -2x + 8
\]
\[
-3(x + 2y) = -3x - 6y
\]

### Step 2: Combine like terms
Now, combine all terms:
\[
-2x + 8 - 3x - 6y = -5x - 6y + 8
\]

This simplifies to:
\[
-5x - 6y + 8
\]

### Simplified Expression: 
\[
-5x - 6y + 8
\]

Would you like more details or have any questions?  
Here are some related questions you might find helpful:
1. How do you solve a system of linear equations involving two variables?
2. Can you explain how to solve word problems involving age or population comparisons?
3. How do you distribute negative signs when simplifying algebraic expressions?
4. Can we solve a similar problem involving three unknowns?
5. How do you check your answer when solving for unknown variables?

**Tip**: Always double-check your final solution by substituting the values back into the original problem to ensure they satisfy all conditions!

There are 8 more male students than females in a college level math class. This total number of students in the class is 26. Find the number of male and female students. Clear parenthesis and combine like terms. −2(x−4) −3(x+2y) Show all the work.

Learn how to find the number of male and female students in a math class using algebraic equations and simplify the expression −2(x−4) −3(x+2y). This problem demonstrates linear equations and the distributive property, suitable for Grades 9-12.

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