To solve the equation \( 8 = 2(10 + 3c) \), let's follow these steps:

### Step 1: Expand the equation
Distribute the \( 2 \) on the right-hand side:

\[
8 = 2 \times 10 + 2 \times 3c
\]
\[
8 = 20 + 6c
\]

### Step 2: Isolate the variable term
Subtract \( 20 \) from both sides to isolate the term with \( c \):

\[
8 - 20 = 6c
\]
\[
-12 = 6c
\]

### Step 3: Solve for \( c \)
Divide both sides by \( 6 \) to solve for \( c \):

\[
c = \frac{-12}{6}
\]
\[
c = -2
\]

### Final Answer:
\( c = -2 \).

Would you like a detailed explanation of any step, or have any questions?

Here are 5 related questions:
1. How do you solve for variables in equations with parentheses?
2. How can you verify your solution after solving for a variable?
3. What happens when equations include fractions or decimals?
4. How does factoring affect the process of solving equations?
5. How do you handle equations with multiple variables?

**Tip:** Always double-check your result by plugging the value of the variable back into the original equation to verify if both sides are equal.

Learn how to solve the linear equation 8 = 2(10 + 3c) with a detailed step-by-step solution. This problem demonstrates key algebraic concepts like the distributive property and basic techniques for isolating variables. Suitable for students in Grades 6-8.

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