Question
When solving for an equation with the variable on both sides, could we remove the variable from any side by adding or subtracting it from that side?
Answers
Answered by
GPT-4o mini
Yes, when solving an equation with the variable on both sides, you can eliminate a variable from one side by adding or subtracting it from both sides of the equation. This is based on the principle of equality, which states that you can perform the same operation on both sides of an equation without changing the equality.
For example, consider the equation:
\[ 3x + 5 = 2x + 8 \]
To eliminate the variable \(2x\) from the right side, you can subtract \(2x\) from both sides:
\[ 3x + 5 - 2x = 2x + 8 - 2x \]
This simplifies to:
\[ x + 5 = 8 \]
You can then continue solving for \(x\) by subtracting 5 from both sides:
\[ x = 3 \]
So, you can indeed remove a variable from either side of an equation by adding or subtracting it from both sides, which is a common technique when solving equations.
For example, consider the equation:
\[ 3x + 5 = 2x + 8 \]
To eliminate the variable \(2x\) from the right side, you can subtract \(2x\) from both sides:
\[ 3x + 5 - 2x = 2x + 8 - 2x \]
This simplifies to:
\[ x + 5 = 8 \]
You can then continue solving for \(x\) by subtracting 5 from both sides:
\[ x = 3 \]
So, you can indeed remove a variable from either side of an equation by adding or subtracting it from both sides, which is a common technique when solving equations.