https://r2.erweima.ai/mathbot/image/172621188259086fn3mdt.jpg

Let's solve each of the equations step-by-step to find the value of \( x \).

### Part A (Top Left):
1. **Equation 1**: \( x - (2 - 3) = 2 \)  
   Simplify: \( x - (-1) = 2 \)  
   \( x + 1 = 2 \)  
   \( x = 1 \)

2. **Equation 2**: \( x - (2 - 4) = 4 \)  
   Simplify: \( x - (-2) = 4 \)  
   \( x + 2 = 4 \)  
   \( x = 2 \)

3. **Equation 3**: \( x - (2 - 5) = 6 \)  
   Simplify: \( x - (-3) = 6 \)  
   \( x + 3 = 6 \)  
   \( x = 3 \)

4. **Equation 4**: \( x - (2 - 6) = 8 \)  
   Simplify: \( x - (-4) = 8 \)  
   \( x + 4 = 8 \)  
   \( x = 4 \)

### Part B (Top Right):
1. **Equation 1**: \( x - (-2 - 3) = 2 \)  
   Simplify: \( x - (-5) = 2 \)  
   \( x + 5 = 2 \)  
   \( x = -3 \)

2. **Equation 2**: \( x - (-2 - 4) = 4 \)  
   Simplify: \( x - (-6) = 4 \)  
   \( x + 6 = 4 \)  
   \( x = -2 \)

3. **Equation 3**: \( x - (-2 - 5) = 6 \)  
   Simplify: \( x - (-7) = 6 \)  
   \( x + 7 = 6 \)  
   \( x = -1 \)

4. **Equation 4**: \( x - (-2 - 6) = 8 \)  
   Simplify: \( x - (-8) = 8 \)  
   \( x + 8 = 8 \)  
   \( x = 0 \)

### Part A (Bottom Left):
1. **Equation 1**: \( 10 - 5(4 - 2x) = 40 \)  
   Expand: \( 10 - 20 + 10x = 40 \)  
   Simplify: \( 10x - 10 = 40 \)  
   \( 10x = 50 \)  
   \( x = 5 \)

2. **Equation 2**: \( 20 - 5(4 - 2x) = 60 \)  
   Expand: \( 20 - 20 + 10x = 60 \)  
   Simplify: \( 10x = 60 \)  
   \( x = 6 \)

3. **Equation 3**: \( 30 - 5(4 - 2x) = 80 \)  
   Expand: \( 30 - 20 + 10x = 80 \)  
   Simplify: \( 10x + 10 = 80 \)  
   \( 10x = 70 \)  
   \( x = 7 \)

4. **Equation 4**: \( 40 - 5(4 - 2x) = 100 \)  
   Expand: \( 40 - 20 + 10x = 100 \)  
   Simplify: \( 10x + 20 = 100 \)  
   \( 10x = 80 \)  
   \( x = 8 \)

### Part B (Bottom Right):
1. **Equation 1**: \( -10(4 - 5x) = 5 \)  
   Expand: \( -40 + 50x = 5 \)  
   Simplify: \( 50x = 45 \)  
   \( x = \frac{45}{50} = 0.9 \)

2. **Equation 2**: \( -12(1 - 5x) = 6 \)  
   Expand: \( -12 + 60x = 6 \)  
   Simplify: \( 60x = 18 \)  
   \( x = \frac{18}{60} = 0.3 \)

3. **Equation 3**: \( -14(-2 - 5x) = 7 \)  
   Expand: \( 28 + 70x = 7 \)  
   Simplify: \( 70x = -21 \)  
   \( x = \frac{-21}{70} = -0.3 \)

4. **Equation 4**: \( -16(-5 - 5x) = 8 \)  
   Expand: \( 80 + 80x = 8 \)  
   Simplify: \( 80x = -72 \)  
   \( x = \frac{-72}{80} = -0.9 \)

Would you like further explanations or have any questions?

### Questions to Consider:
1. What happens when equations include negative numbers?
2. How do parentheses affect the solution of an equation?
3. What is the process for solving linear equations involving fractions?
4. How do we simplify expressions inside the parentheses?
5. How can these methods be applied to more complex algebraic problems?

**Tip:** Always simplify inside parentheses before dealing with the rest of the equation.

Bestimme x for the given set of equations (shown in the image).

Learn how to solve various linear equations step by step, simplifying expressions with parentheses and solving for x. This exercise demonstrates algebraic techniques and the distributive property, suitable for students in Grades 7-9.

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