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Let's solve each of the given linear equations step-by-step:

### a. \( 7 - x = 8 \)
1. Subtract 7 from both sides:
   \[
   7 - x - 7 = 8 - 7
   \]
   \[
   -x = 1
   \]
2. Multiply both sides by -1:
   \[
   x = -1
   \]
   So, \( x = -1 \).

### b. \( 8 - x = 7 \)
1. Subtract 8 from both sides:
   \[
   8 - x - 8 = 7 - 8
   \]
   \[
   -x = -1
   \]
2. Multiply both sides by -1:
   \[
   x = 1
   \]
   So, \( x = 1 \).

### c. \( 5 - x = 5 \)
1. Subtract 5 from both sides:
   \[
   5 - x - 5 = 5 - 5
   \]
   \[
   -x = 0
   \]
2. Multiply both sides by -1:
   \[
   x = 0
   \]
   So, \( x = 0 \).

### d. \( 5 - x = 0 \)
1. Subtract 5 from both sides:
   \[
   5 - x - 5 = 0 - 5
   \]
   \[
   -x = -5
   \]
2. Multiply both sides by -1:
   \[
   x = 5
   \]
   So, \( x = 5 \).

### e. \( 15.3 = 6.7 - x \)
1. Subtract 6.7 from both sides:
   \[
   15.3 - 6.7 = 6.7 - 6.7 - x
   \]
   \[
   8.6 = -x
   \]
2. Multiply both sides by -1:
   \[
   x = -8.6
   \]
   So, \( x = -8.6 \).

### f. \( 5.1 = 4.2 - x \)
1. Subtract 4.2 from both sides:
   \[
   5.1 - 4.2 = 4.2 - 4.2 - x
   \]
   \[
   0.9 = -x
   \]
2. Multiply both sides by -1:
   \[
   x = -0.9
   \]
   So, \( x = -0.9 \).

### Summary
- \( a. x = -1 \)
- \( b. x = 1 \)
- \( c. x = 0 \)
- \( d. x = 5 \)
- \( e. x = -8.6 \)
- \( f. x = -0.9 \)

Would you like more details on any specific solution or have any questions? Here are some related questions you might ask:

1. How do you solve equations with variables on both sides?
2. Can you explain the concept of absolute value equations?
3. What is the method to solve equations with fractional coefficients?
4. How do you solve multi-step linear equations?
5. Can you show examples of linear equations with no solutions or infinite solutions?

### Tip
Always check your solutions by substituting the value of the variable back into the original equation to ensure both sides are equal.

Learn how to solve basic linear equations with detailed step-by-step solutions for equations like 7 - x = 8 and 5.1 = 4.2 - x. This guide covers essential algebraic concepts for students in Grades 6-8.

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