Let's solve the equation \( 13g + 14 = 6g - 6 + 90 \).

### Step 1: Simplify both sides.
On the right-hand side, simplify the expression \( -6 + 90 \):
\[
6g - 6 + 90 = 6g + 84
\]
Now the equation becomes:
\[
13g + 14 = 6g + 84
\]

### Step 2: Move all the terms involving \( g \) to one side.
Subtract \( 6g \) from both sides:
\[
13g - 6g + 14 = 84
\]
\[
7g + 14 = 84
\]

### Step 3: Move the constant term to the other side.
Subtract 14 from both sides:
\[
7g = 84 - 14
\]
\[
7g = 70
\]

### Step 4: Solve for \( g \).
Divide both sides by 7:
\[
g = \frac{70}{7}
\]
\[
g = 10
\]

### Final Answer: \( g = 10 \).

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you solve equations with variables on both sides?
2. What happens if an equation has no solutions or infinite solutions?
3. How can you check if your solution to an equation is correct?
4. What are common mistakes to avoid when solving equations?
5. Can you solve this equation for \( g \) if the constants were different?

**Tip:** Always simplify both sides of the equation first to avoid mistakes.

Learn how to solve the linear equation 13g + 14 = 6g - 6 + 90 with a step-by-step solution. This problem demonstrates key algebraic concepts such as simplifying both sides of the equation and solving for the variable g. Suitable for students in Grades 7-9.

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