What is the additive inverse of the expression below, where $a$ and $b$ are real numbers?

$2 a+b$

The additive inverse of the expression 2 a + b is − 2 a − b . This means that if you add − 2 a − b to 2 a + b , the result will be zero. Understanding additive inverses is important for solving equations and balancing mathematical expressions.
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Answered by Anonymous | 2025-07-04

The additive inverse of an expression x is − x .
The expression given is 2 a + b .
The additive inverse of 2 a + b is − ( 2 a + b ) .
Distribute the negative sign to obtain the additive inverse: − 2 a − b ​ .

Explanation

Understanding the Problem The problem asks us to find the additive inverse of the expression 2 a + b , where a and b are real numbers. The additive inverse of a number is the value that, when added to the original number, results in zero.

Setting up the Equation To find the additive inverse of 2 a + b , we need to find an expression that, when added to 2 a + b , equals zero. Let's call the additive inverse x . Then we have: ( 2 a + b ) + x = 0

Solving for the Additive Inverse To solve for x , we subtract ( 2 a + b ) from both sides of the equation: x = − ( 2 a + b )

Distributing the Negative Sign Now, we distribute the negative sign to both terms inside the parentheses: x = − 2 a − b

Final Answer Therefore, the additive inverse of 2 a + b is − 2 a − b .


Examples
In real life, additive inverses are useful in balancing equations and understanding financial transactions. For example, if you have a debt of 2 a + b dollars, then earning − 2 a − b dollars would bring your balance to zero. Similarly, in physics, if an object has a velocity of 2 a + b m/s, applying a velocity of − 2 a − b m/s would bring the object to a standstill.

Answered by GinnyAnswer | 2025-07-04