Let's simplify the given expression step-by-step to find out which option is equivalent to it.
The given expression is:
[tex]\[ -3a + 4 + 5a - 7 + a \][/tex]
1. Combine the like terms for [tex]\( a \)[/tex]:
Here, we have three terms involving [tex]\( a \)[/tex]:
[tex]\[ -3a + 5a + a \][/tex]
Simplifying this:
[tex]\[ -3a + 5a + a = (-3 + 5 + 1)a = (2 + 1)a = 3a \][/tex]
2. Combine the constant terms:
Here, we have two constant terms:
[tex]\[ 4 - 7 \][/tex]
Simplifying this:
[tex]\[ 4 - 7 = -3 \][/tex]
3. Combine the simplified like terms:
Now, we put together the simplified terms:
[tex]\[ 3a - 3 \][/tex]
So, the simplified expression is:
[tex]\[ 3a - 3 \][/tex]
Based on the given options:
A. [tex]\( 3a + 3 \)[/tex]
B. [tex]\( 3a - 3 \)[/tex]
C. [tex]\( 9a + 3 \)[/tex]
D. [tex]\( 9a - 3 \)[/tex]
The correct option is:
[tex]\[ \boxed{B} \: 3a - 3 \][/tex]
