To understand how Step 3 helps solve the equation \(4x - 12 = 20\), we need to clarify what the step is and how it fits into the overall process of solving the equation.
Here's a brief breakdown of the steps you've provided:
- Step 1: Start with the original equation: \(4x - 12 = 20\).
- Step 2: Add 12 to both sides: \(4x - 12 + 12 = 20 + 12\), which simplifies to \(4x = 32\). This step effectively isolates the term involving the variable \(x\) by eliminating the \(-12\).
- Step 3: You would then divide both sides by 4: \( \frac{4x}{4} = \frac{32}{4}\), resulting in \(x = 8\). This step isolates the variable \(x\) by removing the coefficient (4) that is affecting \(x\).
Now, looking specifically at Step 3:
The statement "Dividing both sides by 4 isolates the variable" correctly describes how Step 3 functions. By dividing both sides of the equation by 4, you eliminate the coefficient of \(x\), which allows you to solve for \(x\) directly.
So, to explain how Step 3 helps solve the equation:
Step 3 is crucial because it simplifies the equation to a state where \(x\) stands alone on one side. After isolating \(x\), you can immediately determine its value. If you didn't perform this division, \(x\) would still be tied to the number 4, making it impossible to find the exact value of \(x\). Thus, Step 3 enables you to arrive at the final solution of the equation, which is \(x = 8\).
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