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.

Learn how to solve the equation |5x+5|−16=0 step-by-step with clear explanations and examples. Understand the concept of absolute value in equations and solve for x using basic algebraic methods. Suitable for Grades 7-9 students.

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