To solve the equation \( 5x + 6 = 10 - 2x \), follow these steps:

### Step 1: Combine like terms by moving all terms involving \( x \) to one side.
Add \( 2x \) to both sides:
\[
5x + 2x + 6 = 10
\]
This simplifies to:
\[
7x + 6 = 10
\]

### Step 2: Move constants to the other side.
Subtract 6 from both sides:
\[
7x = 10 - 6
\]
\[
7x = 4
\]

### Step 3: Solve for \( x \).
Divide both sides by 7:
\[
x = \frac{4}{7}
\]

So, the solution is \( x = \frac{4}{7} \).

Would you like further clarification on any steps?

Here are 5 related questions you might want to explore:
1. How do you solve the equation \( 3x + 5 = 2x - 4 \)?
2. What happens if you have variables on both sides and fractions involved?
3. How do you solve an equation with quadratic terms?
4. How would you check if your solution to the equation is correct?
5. What is the importance of isolating the variable in algebraic equations?

**Tip**: Always simplify both sides of an equation first before solving for the unknown variable.

Learn how to solve the linear equation 5x + 6 = 10 - 2x step by step. This problem focuses on key algebraic concepts like equation balancing, combining like terms, and solving for the variable x. Suitable for students in Grades 6-8.

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