Question

Which equation has NO SOLUTION?

Responses

- 5x + 9 = 2x + 9 - 7x
- 5x + 9 = 2x + 9 - 7x EndFragment

9x + 9 = 11x - 2x + 9
9x + 9 = 11x - 2x + 9 EndFragment

7x + 30 = x + 6 (x + 5)
7x + 30 = x + 6 (x + 5) EndFragment

7x -6 = x + 6 (x + 5)

Answer 1

To determine which equation has no solution, we can solve each equation.

1. **Equation 1: \(5x + 9 = 2x + 9 - 7x\)**

Simplifying the right side:
\[
2x + 9 - 7x = -5x + 9
\]
So, we rewrite the equation:
\[
5x + 9 = -5x + 9
\]
Now, add \(5x\) to both sides:
\[
10x + 9 = 9
\]
Subtract \(9\) from both sides:
\[
10x = 0 \implies x = 0
\]
This equation has a solution: \(x = 0\).

2. **Equation 2: \(9x + 9 = 11x - 2x + 9\)**

Simplifying the right side:
\[
11x - 2x + 9 = 9x + 9
\]
So we rewrite the equation:
\[
9x + 9 = 9x + 9
\]
This simplifies to:
\[
0 = 0
\]
This is an identity, meaning it has infinitely many solutions.

3. **Equation 3: \(7x + 30 = x + 6(x + 5)\)**

Expanding the right side:
\[
6(x + 5) = 6x + 30,
\]
so we have:
\[
7x + 30 = x + 6x + 30 \implies 7x + 30 = 7x + 30.
\]
This also simplifies to:
\[
0 = 0.
\]
Again, this is an identity, meaning it has infinitely many solutions.

4. **Equation 4: \(7x - 6 = x + 6(x + 5)\)**

Expanding the right side:
\[
6(x + 5) = 6x + 30,
\]
so we rewrite the equation:
\[
7x - 6 = x + 6x + 30 \implies 7x - 6 = 7x + 30.
\]
Now let's simplify:
Subtract \(7x\) from both sides:
\[
-6 = 30.
\]
This is a contradiction (false statement), meaning there is no solution.

Based on the analysis, the equation that has **no solution** is:

**\(7x - 6 = x + 6(x + 5)\)**