Let's analyze the equation step by step and identify the properties or operations used to solve each equation:
Original Equation:
\[ 5 - 3(x + 3) = 11 - 8x \]
Step 1: 5x = 15
This step appears to be incorrect if derived from the original equation, as we will see in the subsequent steps. I believe there might have been an error in stating the equation or the steps.
Step 2: 5 - 3x - 9 = 11 - 8x
- Distributive Property: Distributing \(-3\) across the \((x + 3)\) gives \(-3x - 9\).
- Simplification: Combine \(5 - 9\) to get \(-4\), so the left side becomes \(-4 - 3x\).
So this step can be expressed as: \[ 5 - 3(x + 3) = 11 - 8x \implies 5 - 3x - 9 = 11 - 8x \]
Step 3: x = 3
At this point, it seems that we do not have a clear transition from the previous steps to this result directly. Typically, we would isolate \(x\) by adding or subtracting terms then dividing or multiplying.
Let's assume combining terms is occurring which reveals \(x\):
- Isolation of Variable: You would need to manipulate to get to \(x\) from the prior step, which likely would involve moving terms involving \(x\) to one side and constants to the other.
- This would be through Addition to both sides or Subtraction of whole entities.
Step 4: 5x - 4 = 11
If this is derived from the previous incorrect statements:
- Adding or Subtracting: The goal is to arrange it into a standard algebraic form.
Step 5: -3x - 4 = 11 - 8x
This seems to rearrange terms again:
- Transposition of Terms: Moving terms from one side to another while changing their signs.
Summary of Steps
- Distributive Property: Used when distributing \(-3\) in Step 2.
- Combining Like Terms: In the manipulations occurring to isolate \(x\).
- Addition or Subtraction: When both sides of the equation are manipulated to isolate variables.
Cloistered
The steps provided seem not to correlate directly; hence reviewing the original equation might present alternate ways to achieve \(x\). Please confirm the integrity of the original equation and the steps so the manipulations can be aligned to achieve accuracy.
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