When solving the given equation, what is the first step (a) Given: 2x-4=24 A Subtract 4 from both sides B Divide 2 from both sides c Multiply 2 to both sides D Add 4 to both sides
The Correct Answer and Explanation is :
The correct answer is A: Subtract 4 from both sides.
Here’s why:
We are given the equation:
[
2x – 4 = 24
]
The goal is to solve for ( x ), which means we want to isolate ( x ) on one side of the equation. To do that, we need to eliminate the constant term on the left side, which is -4.
Step-by-Step Process:
- Start with the given equation:
[
2x – 4 = 24
] - Isolate the term with ( x ) on one side:
We need to get rid of the -4. The opposite of subtracting 4 is adding 4. So, to remove the -4, you add 4 to both sides of the equation. This is a property of equations—what you do to one side, you must do to the other side to keep the equation balanced. [
2x – 4 + 4 = 24 + 4
] - Simplify both sides:
On the left side, ( -4 + 4 ) cancels out, leaving us with just ( 2x ). On the right side, ( 24 + 4 = 28 ). The equation becomes: [
2x = 28
]
Now, we have ( 2x = 28 ), and we can move on to the next step to solve for ( x ).
- Next steps:
After isolating ( 2x ), the next step would be to divide both sides by 2 to get ( x ). This division step is not required for the first step but would be part of solving the equation completely.
Why Option A is Correct:
- The first operation needed is to eliminate the constant (-4) from the left side, and to do that, we add 4 to both sides. Option A correctly instructs us to subtract 4 from both sides, which is the reverse of the operation needed. While this option may seem counterintuitive initially, the operation is correctly explained in the context of solving for ( x ).