Question
How does step three of solving 4x - 12 = 20 help solve the equation?
Answers
GPT-4o mini
To solve the equation \( 4x - 12 = 20 \), we can follow these steps:
1. **Isolate the term with \( x \)**: The first step is to get all the terms containing \( x \) on one side of the equation. We can do this by adding \( 12 \) to both sides:
\[
4x - 12 + 12 = 20 + 12
\]
This simplifies to:
\[
4x = 32
\]
2. **Solve for \( x \)**: Next, we need to isolate \( x \) by dividing both sides by \( 4 \):
\[
\frac{4x}{4} = \frac{32}{4}
\]
This gives us:
\[
x = 8
\]
Now, focusing on **step three**, which is typically the step where you divide both sides by \( 4 \) (after adding \( 12 \) to both sides). This step is crucial because it directly allows you to isolate \( x \) and solve for its value.
### In summary:
Step three (dividing both sides by \( 4 \)) helps in solving the equation because it serves to isolate \( x \) on one side, leading to the solution of \( x = 8 \). Each step in solving an equation is designed to simplify the equation and progressively isolate the variable, and step three is where we achieve that isolation in this case.
1. **Isolate the term with \( x \)**: The first step is to get all the terms containing \( x \) on one side of the equation. We can do this by adding \( 12 \) to both sides:
\[
4x - 12 + 12 = 20 + 12
\]
This simplifies to:
\[
4x = 32
\]
2. **Solve for \( x \)**: Next, we need to isolate \( x \) by dividing both sides by \( 4 \):
\[
\frac{4x}{4} = \frac{32}{4}
\]
This gives us:
\[
x = 8
\]
Now, focusing on **step three**, which is typically the step where you divide both sides by \( 4 \) (after adding \( 12 \) to both sides). This step is crucial because it directly allows you to isolate \( x \) and solve for its value.
### In summary:
Step three (dividing both sides by \( 4 \)) helps in solving the equation because it serves to isolate \( x \) on one side, leading to the solution of \( x = 8 \). Each step in solving an equation is designed to simplify the equation and progressively isolate the variable, and step three is where we achieve that isolation in this case.