2x + 4 =what is the answer?
The Correct Answer and Explanation is :
To solve the equation (2x + 4 = 0), we first isolate the variable (x).
Step 1: Subtract 4 from both sides
We start by moving the constant term (4) to the other side of the equation. This gives us:
[
2x + 4 – 4 = 0 – 4
]
Simplifying this, we have:
[
2x = -4
]
Step 2: Divide both sides by 2
Next, we need to solve for (x) by dividing both sides of the equation by 2:
[
\frac{2x}{2} = \frac{-4}{2}
]
This simplifies to:
[
x = -2
]
Conclusion
Thus, the solution to the equation (2x + 4 = 0) is (x = -2).
Explanation
In algebra, an equation is a statement that two expressions are equal. To solve for a variable, we manipulate the equation to isolate the variable on one side. In this case, we started with the equation (2x + 4) set equal to zero. The first step was to eliminate the constant term (4) from the left side, which involved subtracting 4 from both sides of the equation. This step is crucial as it maintains the equality of both sides.
Next, we had to isolate (x) by removing the coefficient (2) in front of (x). We achieved this by dividing both sides by 2. This operation is valid because dividing or multiplying both sides of an equation by the same non-zero number does not change the equality.
The result, (x = -2), tells us the value of (x) that makes the original equation true. Checking our work, if we substitute (-2) back into the original equation, we get (2(-2) + 4 = -4 + 4 = 0), confirming that our solution is correct. This process of solving equations is foundational in algebra, allowing us to work with unknowns and find their values.