Solve for $a$. $P=a+b-1$
Answer (2)
Start with the given equation: P = a + b − 1 .
Isolate a by subtracting b and adding 1 to both sides: P − b + 1 = a + b − 1 − b + 1 .
Simplify the equation to find a : a = P − b + 1 .
The solution for a is: a = P − b + 1 .
Explanation
Understanding the equation We are given the equation P = a + b − 1 and we want to isolate a to solve for it.
Isolating a To isolate a , we need to subtract b from both sides of the equation and add 1 to both sides. This gives us:
P − b + 1 = a + b − 1 − b + 1
Simplifying the right side, we get:
P − b + 1 = a
Final Answer Therefore, we have solved for a in terms of P and b .
a = P − b + 1
Examples
In physics, you might use this formula to find the initial position ( a ) of an object given its final position ( P ), the displacement ( b ), and accounting for a constant offset (-1). For example, if an object's final position is 10 meters ( P = 10 ), and it moved 3 meters ( b = 3 ) from its initial position, then its initial position would be a = 10 − 3 + 1 = 8 meters. This kind of algebraic manipulation is useful in various fields to rearrange formulas and solve for unknown variables.
To solve for a in the equation P = a + b − 1 , we isolate a by rewriting the equation to get a = P − b + 1 . This allows us to express a in terms of values P and b . The final answer is a = P − b + 1 .
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