Let's solve the equation \( \frac{1}{4}(2x + 8) = -4 \).

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 4 to get rid of the fraction:

\[
1 \cdot (2x + 8) = -4 \times 4
\]

\[
2x + 8 = -16
\]

### Step 2: Isolate the variable term
Subtract 8 from both sides:

\[
2x = -16 - 8
\]

\[
2x = -24
\]

### Step 3: Solve for \( x \)
Divide both sides by 2:

\[
x = \frac{-24}{2}
\]

\[
x = -12
\]

So, the solution is \( x = -12 \).

Would you like further details or have any questions?

Here are 8 related questions to expand your understanding:
1. What if the equation was \( \frac{1}{3}(3x + 9) = -5 \)?
2. How do you solve \( \frac{1}{2}(4x - 10) = 6 \)?
3. What happens if you add 3 to both sides of the equation?
4. Can you solve \( 5x + 7 = 2x - 9 \)?
5. What if the equation included a negative fraction, like \( \frac{-1}{4}(2x + 8) = -4 \)?
6. How would the solution change if the equation was \( \frac{1}{4}(2x + 8) = 0 \)?
7. What does it mean to isolate the variable in an equation?
8. How would you solve the equation \( \frac{1}{2}(2x + 6) = 5 \)?

**Tip:** When dealing with equations that have fractions, it's often helpful to eliminate the fraction first by multiplying both sides by the denominator.

Learn how to solve the equation 1/4(2x + 8) = -4 with a detailed step-by-step solution. This problem involves equations with fractions and isolating variables. Suitable for students in Grades 7-9.

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