To determine the additive inverse of an expression, it's crucial to understand what we mean by "additive inverse." For any given expression, its additive inverse is the expression that, when added to the original expression, results in zero.
Let's consider the expression given:
[tex]\[ 2a + b \][/tex]
Our goal is to find another expression that, when added to [tex]\( 2a + b \)[/tex], will result in zero.
1. Start by writing the original expression:
[tex]\[ 2a + b \][/tex]
2. To find the additive inverse, think about what needs to be added to [tex]\( 2a + b \)[/tex] to get zero. Let's denote the additive inverse by [tex]\( x \)[/tex]. Therefore, we need:
[tex]\[ 2a + b + x = 0 \][/tex]
3. Solving for [tex]\( x \)[/tex], we can subtract [tex]\( 2a + b \)[/tex] from both sides of the equation:
[tex]\[ x = -(2a + b) \][/tex]
4. Simplify the right side of the equation:
[tex]\[ x = -2a - b \][/tex]
Thus, the additive inverse of the expression [tex]\( 2a + b \)[/tex] is [tex]\( -2a - b \)[/tex].
Given the choices:
- [tex]\( -1 \)[/tex]
- [tex]\( 0 \)[/tex]
- [tex]\( 2a - b \)[/tex]
- [tex]\( -2a - b \)[/tex]
The correct answer is:
[tex]\[ -2a - b \][/tex]
So, the additive inverse of [tex]\( 2a + b \)[/tex] is [tex]\( -2a - b \)[/tex].
