To solve the equation \( |5x + 8| = 3x \), we need to consider two cases because the absolute value can make the expression inside positive or negative. 

### Case 1: \( 5x + 8 = 3x \)

1. Subtract \( 3x \) from both sides:
   \[
   5x - 3x + 8 = 0
   \]
   \[
   2x + 8 = 0
   \]

2. Subtract 8 from both sides:
   \[
   2x = -8
   \]

3. Divide both sides by 2:
   \[
   x = -4
   \]

### Case 2: \( 5x + 8 = -3x \)

1. Add \( 3x \) to both sides:
   \[
   5x + 3x + 8 = 0
   \]
   \[
   8x + 8 = 0
   \]

2. Subtract 8 from both sides:
   \[
   8x = -8
   \]

3. Divide both sides by 8:
   \[
   x = -1
   \]

### Check the solutions:

- For \( x = -4 \):
  \[
  |5(-4) + 8| = 3(-4)
  \]
  \[
  |-20 + 8| = -12
  \]
  \[
  |-12| = -12
  \]
  This is not true, so \( x = -4 \) is not a solution.

- For \( x = -1 \):
  \[
  |5(-1) + 8| = 3(-1)
  \]
  \[
  |-5 + 8| = -3
  \]
  \[
  |3| = -3
  \]
  This is also not true.

### Conclusion:
There are no solutions to the equation \( |5x + 8| = 3x \).

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. Solve \( |2x + 7| = 4x \).
2. Solve \( |3x - 5| = 2x \).
3. Solve \( |x + 1| = 2x - 3 \).
4. Solve \( |x - 3| = x + 1 \).
5. Solve \( |x - 4| = -x \).

**Tip:** Always check both cases when dealing with absolute value equations to ensure valid solutions.

Learn how to solve the absolute value equation ∣5x + 8∣ = 3x with a detailed step-by-step solution. This problem covers key algebraic concepts and properties of absolute values. Suitable for students in Grades 9-11.

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