Question

Complete the steps for the single variable linear equation below.
9x + 5 = 10(x+3) - x

Solve for x
1. Be sure to show your work.
2. State whether the single variable linear equation has a solution, no solution, or infinitely many solutions.
3. Explain your answer in step 2.

Answer 1

can you make it less advanced and use less words

Answer 2

To solve the single variable linear equation \( 9x + 5 = 10(x+3) - x \), we will proceed step by step.

### Step 1: Distribute and Simplify

Start by distributing the \(10\) on the right side of the equation:

\[
10(x + 3) = 10x + 30
\]

Now, substitute that back into the equation:

\[
9x + 5 = 10x + 30 - x
\]

### Step 2: Combine Like Terms

Next, we simplify the right side by combining like terms:

\[
10x - x = 9x
\]

Thus, the equation becomes:

\[
9x + 5 = 9x + 30
\]

### Step 3: Isolate Terms

Now, let's isolate the variable terms by subtracting \(9x\) from both sides:

\[
9x + 5 - 9x = 9x + 30 - 9x
\]

This simplifies to:

\[
5 = 30
\]

### Step 4: Analyze the Result

The equation \(5 = 30\) is a contradiction; it is never true.

### Step 5: State the Solution Type

Since we reached a contradiction while solving the equation, we conclude that:

- **No Solution**: The linear equation does not hold true for any value of \(x\).

### Step 6: Explanation

In this case, we started with a valid linear equation; however, through the steps of solving, we found that it simplifies to an impossibility (5 being equal to 30), indicating that there are no values of \(x\) that can satisfy the original equation. Thus, we declare that the equation has **no solution**.

Answer 3

Sure! Here’s a simpler version:

**Given Equation:**
\[ 9x + 5 = 10(x + 3) - x \]

**Step 1: Distribute**
\[ 10(x + 3) = 10x + 30 \]
So, the equation becomes:
\[ 9x + 5 = 10x + 30 - x \]

**Step 2: Simplify Right Side**
Combine \(10x\) and \(-x\):
\[ 10x - x = 9x \]
Now the equation is:
\[ 9x + 5 = 9x + 30 \]

**Step 3: Subtract \(9x\) from Both Sides**
\[ 9x + 5 - 9x = 9x + 30 - 9x \]
This simplifies to:
\[ 5 = 30 \]

**Step 4: Conclusion**
Since \(5\) is not equal to \(30\), there is **no solution** to this equation.

### Explanation:
The equation leads to a false statement, so there are no values for \(x\) that make it true.