Let's solve the equation \( x + 2(x - 7) = 3x - 7 \).

### Step 1: Distribute the \( 2 \) on the left-hand side
\[
x + 2(x - 7) = x + 2x - 14
\]
So the equation becomes:
\[
x + 2x - 14 = 3x - 7
\]

### Step 2: Combine like terms on both sides
\[
3x - 14 = 3x - 7
\]

### Step 3: Subtract \( 3x \) from both sides
\[
-14 = -7
\]

This results in a **contradiction** because \(-14 \neq -7\). Therefore, there is **no solution** to this equation.

This is called an **inconsistent equation**, meaning it has no possible value for \( x \) that will satisfy the equation.

Would you like further explanation or have any other questions?

Here are 5 related questions:
1. What is the difference between inconsistent and consistent equations?
2. How can you tell if an equation has no solution before solving?
3. What happens if both sides of an equation are identical after simplification?
4. How do you solve equations with variables on both sides?
5. Can equations with fractions have no solution as well?

**Tip:** Always simplify equations as much as possible before trying to isolate variables to catch potential contradictions early.

Discover how to solve the linear equation x + 2(x - 7) = 3x - 7 with a step-by-step breakdown. Learn about the distributive property and inconsistent equations, and find out why this problem has no solution. Ideal for students in Grades 8-10.

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