A-15=4a-3
The Correct Answer and Explanation is :
To solve the equation ( A – 15 = 4a – 3 ), we need to isolate the variable ( A ) on one side of the equation. Here’s a step-by-step breakdown:
Step 1: Start with the given equation
[
A – 15 = 4a – 3
]
Step 2: Add 15 to both sides
In order to isolate ( A ), we want to eliminate the ( -15 ) on the left side. We can do this by adding 15 to both sides of the equation. This gives:
[
A – 15 + 15 = 4a – 3 + 15
]
Simplifying both sides:
[
A = 4a + 12
]
Final Answer:
[
A = 4a + 12
]
Explanation:
This is a linear equation, and we used the basic principle of solving equations: maintaining balance by performing the same operation on both sides. Here’s why the steps are valid:
- Adding 15 to both sides: The goal was to move the constant term (-15) from the left-hand side of the equation to the right-hand side. By doing this, we keep the equation balanced, meaning both sides still represent the same value.
- Simplifying the expression: After adding 15, we combine like terms to simplify the equation, giving us the expression ( A = 4a + 12 ). This equation tells us that ( A ) is equal to 4 times ( a ), plus 12.
Context:
Linear equations like this one are fundamental in algebra because they demonstrate how variables and constants interact. The equation is solved by systematically isolating the unknown variable. The process of isolating the variable involves using basic operations such as addition, subtraction, multiplication, and division, ensuring that both sides of the equation stay equal.
The solution, ( A = 4a + 12 ), now expresses ( A ) in terms of ( a ), allowing us to compute ( A ) once the value of ( a ) is known.