Please solve –19 = x – 4
The Correct Answer and Explanation is :
To solve the equation (-19 = x – 4), we want to isolate the variable (x). Here’s a step-by-step breakdown of the solution:
Step 1: Understand the Equation
The equation states that (-19) is equal to (x) minus (4). Our goal is to determine the value of (x) that makes this statement true.
Step 2: Isolate (x)
To isolate (x), we need to eliminate the (-4) on the right side of the equation. We can do this by adding (4) to both sides of the equation. The rule of equality tells us that whatever we do to one side of an equation, we must do to the other side to keep it balanced.
[
-19 + 4 = x – 4 + 4
]
Step 3: Simplify Both Sides
Now, let’s simplify both sides:
[
-15 = x
]
Conclusion
The value of (x) is (-15). Therefore, we can say that (-19 = -15 – 4) is true, confirming our solution.
Explanation of the Steps
- Understanding the Equation: It’s crucial to interpret what the equation represents. Here, (x) is the unknown we need to find.
- Applying the Rule of Equality: Adding (4) to both sides ensures that the balance of the equation is maintained. This is a fundamental principle of algebra: whatever operation we perform on one side of the equation, we must perform the same operation on the other side.
- Simplifying: After performing the operation, we simplify both sides to find the value of (x).
- Verifying the Solution: Once we find (x), it’s important to substitute it back into the original equation to ensure that both sides remain equal. This verification process is essential in mathematics to confirm that our solution is correct.
In summary, the solution to the equation (-19 = x – 4) is (x = -15). This method demonstrates basic algebraic manipulation and the principles of equality.