To solve the equation $|5x + 5| - 16 = 0$, follow these steps:

Step 1: Isolate the absolute value expression.

Add 16 to both sides of the equation: $|5x + 5| = 16$

Step 2: Set up two separate equations.

The absolute value equation $|A| = B$ can be split into two cases:

1. $5x + 5 = 16$
2. $5x + 5 = -16$

Step 3: Solve each equation.

For the first equation: $5x + 5 = 16$ Subtract 5 from both sides: $5x = 11$ Divide by 5: $x = \frac{11}{5} = 2.2$

For the second equation: $5x + 5 = -16$ Subtract 5 from both sides: $5x = -21$ Divide by 5: $x = \frac{-21}{5} = -4.2$

Step 4: Write the solution.

The solutions are $x = 2.2$ and $x = -4.2$.

Summary:

The values of $x$ that satisfy the equation $|5x + 5| - 16 = 0$ are $x = 2.2$ and $x = -4.2$.

Would you like more details or have any questions about this solution?

Here are some related questions:

1. What is the general method to solve absolute value equations?
2. How would the solution change if the equation were $|5x + 5| = 0$?
3. What if the equation had an inequality instead of an equal sign?
4. Can you solve $|5x + 5| - 10 = 6$?
5. What are some real-world applications of absolute value equations?
6. How would you graph $|5x + 5| - 16 = 0$?
7. What is the significance of absolute value in mathematics?
8. How would you solve the equation if it included a quadratic term inside the absolute value?

Tip: Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.