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

Question

5x = 15
5 - 3x - 9 = 11 - 8x
x = 3
5x - 4 = 11
-3x - 4 = 11 - 8x

Answer 1

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 2

yes but give the properties of each step.

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 \(x = 3\).