Question

Which of the following table shows the correct steps to factor out the GCF and solve the quadratic equation 7x = 56 x

Answer 1

To factor out the greatest common factor (GCF) and solve the quadratic equation \(7x = 56x\), we first rearrange the equation into standard form:

1. **Rearranging the Equation**:
Move all terms to one side of the equation:
\[ 7x - 56x = 0 \]
\[ -49x = 0 \]

2. **Factoring Out the GCF**:
The GCF of \(7x\) and \(56x\) is \(7x\). We can factor as follows:
\[ 7x(1 - 8) = 0 \]
Here, we factored out \(7x\), but notice that this situation is a little different, as \(56x\) was derived from \(8 \times 7x\).

3. **Setting Factors to Zero**:
Set the remaining factors to zero. We have:
\[ 7x = 0 \]
or
\[ (1 - 8) = 0 \] (since that factor makes no sense, we ignore it).

4. **Solving for x**:
From \(7x = 0\), divide both sides by 7:
\[ x = 0 \]

The solution to the equation \(7x = 56x\) after factoring out the GCF is \(x = 0\).

Please provide the specific table or options you mentioned so I can help you determine which shows the correct steps if needed.