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.