Let's solve the equation step by step:

Given equation:
\[
176 = 13(2 + 6x) - 16(x - 10)
\]

### Step 1: Distribute the constants inside the parentheses.
Distribute \(13\) across \((2 + 6x)\):
\[
13 \times 2 + 13 \times 6x = 26 + 78x
\]
Distribute \(-16\) across \((x - 10)\):
\[
-16 \times x + (-16) \times (-10) = -16x + 160
\]
So the equation becomes:
\[
176 = 26 + 78x - 16x + 160
\]

### Step 2: Combine like terms.
Combine the \(x\) terms and the constant terms on the right side:
\[
176 = (78x - 16x) + (26 + 160)
\]
\[
176 = 62x + 186
\]

### Step 3: Isolate the \(x\) term.
Subtract 186 from both sides:
\[
176 - 186 = 62x
\]
\[
-10 = 62x
\]

### Step 4: Solve for \(x\).
Divide both sides by 62:
\[
x = \frac{-10}{62} = \frac{-5}{31}
\]

So, the solution is:
\[
x = -\frac{5}{31}
\]

Would you like more details on any of these steps, or do you have any questions?

Here are 5 related questions:
1. How do you solve a similar equation with different coefficients?
2. What happens if there is a quadratic term in the equation?
3. How do you check if your solution to an equation is correct?
4. What is the general process for solving linear equations?
5. How do you solve an equation with variables on both sides?

**Tip:** When solving equations, always start by simplifying both sides as much as possible before isolating the variable.

Learn how to solve the linear equation 176 = 13(2 + 6x) - 16(x - 10) step-by-step. This problem involves distributing constants, combining like terms, and isolating the variable. Suitable for students in Grades 7-9.

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