Question

Identify the steps followed to solve the equation: 5 - 3 (x + 3) = 11 - 8x
5x = 15
5 - 3x - 9 = 11 - 8x
x = 3
5x - 4 = 11
-3x - 4 = 11 - 8x

Answer 1

yes but give the properties of each step.

Answer 2

To solve the equation \( 5 - 3 (x + 3) = 11 - 8x \), we can follow these steps along with the transformations you've provided:

1. **Expand the Left Side:**
Start by distributing the \(-3\) on the left side:
\[
5 - 3(x + 3) = 5 - 3x - 9
\]
This simplifies to:
\[
-3x - 4
\]

2. **Set Up the Equation:**
Now, write the equation with the simplified left side:
\[
-3x - 4 = 11 - 8x
\]

3. **Isolate Terms:**
To get all terms involving \(x\) on one side and constant terms on the other side, you can add \(8x\) to both sides:
\[
-3x + 8x - 4 = 11
\]
This simplifies to:
\[
5x - 4 = 11
\]

4. **Solve for x:**
Next, add \(4\) to both sides:
\[
5x = 11 + 4
\]
This becomes:
\[
5x = 15
\]

5. **Divide by Coefficient:**
Finally, divide both sides by \(5\) to solve for \(x\):
\[
x = \frac{15}{5} = 3
\]

Thus, the solution to the equation \(5 - 3 (x + 3) = 11 - 8x\) is \(x = 3\).

### Summary of Steps:
1. Expand the equation.
2. Set it up in a simplified form.
3. Collect like terms.
4. Solve for \(x\).
5. Find the value of \(x\).

You've correctly identified \(x = 3\) as the final answer.

Answer 3

Certainly! Here are the steps to solve the equation \(5 - 3(x + 3) = 11 - 8x\) along with the mathematical properties or rules applied at each step:

### Step 1: Expand the Left Side
**Equation**:
\[
5 - 3(x + 3)
\]

**Transformation**:
Using the **Distributive Property**:
\[
5 - 3x - 9
\]

**Result**:
Combining the constant terms gives:
\[
-3x - 4
\]

### Step 2: Set Up the Equation
**Equation**:
Setting the transformed left side equal to the right side:
\[
-3x - 4 = 11 - 8x
\]

### Step 3: Collect Like Terms
**Transformation**:
Add \(8x\) to both sides to isolate the variable on one side. This uses the **Addition Property of Equality** (if you add the same value to both sides of an equation, the equation remains true):
\[
-3x + 8x - 4 = 11
\]

**Result**:
This simplifies to:
\[
5x - 4 = 11
\]

### Step 4: Isolate the Variable
**Transformation**:
Add \(4\) to both sides to isolate the term with \(x\) on one side. Again, this is using the **Addition Property of Equality**:
\[
5x = 11 + 4
\]

**Result**:
This simplifies to:
\[
5x = 15
\]

### Step 5: Solve for x
**Transformation**:
Divide both sides by \(5\) to solve for \(x\). This step uses the **Division Property of Equality** (dividing both sides of an equation by the same non-zero number keeps the equation balanced):
\[
x = \frac{15}{5}
\]

**Result**:
This gives:
\[
x = 3
\]

### Summary of Properties Used
1. **Distributive Property**: Used for expanding expressions.
2. **Addition Property of Equality**: Used to add the same value to both sides of the equation without changing the equality.
3. **Division Property of Equality**: Used to divide both sides by the same non-zero value to isolate the variable.

By following these steps and applying the respective properties, we arrive at the solution \(x = 3\).