Sure, let's simplify the given expression step-by-step:
### Expression:
[tex]\[ 10y + 12 - 7y - 8 - 3y \][/tex]
### Step 1: Identify and Group Like Terms
In the expression [tex]\( 10y + 12 - 7y - 8 - 3y \)[/tex], we have two types of terms: those with [tex]\( y \)[/tex] and constant terms. We'll group these like terms together.
### Terms with [tex]\( y \)[/tex]:
[tex]\[ 10y, -7y, -3y \][/tex]
### Constant Terms:
[tex]\[ 12, -8 \][/tex]
### Step 2: Combine the Like Terms
First, let's combine the terms containing [tex]\( y \)[/tex]:
[tex]\[ 10y - 7y - 3y \][/tex]
Combine these by adding/subtracting their coefficients:
[tex]\[ 10 - 7 - 3 = 0 \][/tex]
So, [tex]\( 10y - 7y - 3y = 0y \)[/tex]
Next, let's combine the constant terms:
[tex]\[ 12 - 8 \][/tex]
Combine these by adding/subtracting:
[tex]\[ 12 - 8 = 4 \][/tex]
### Step 3: Write the Simplified Expression
Since [tex]\( 0y \)[/tex] is simply 0, we are left with the constant term:
[tex]\[ 4 \][/tex]
Thus, the simplified expression is:
[tex]\[ 4 \][/tex]
### Conclusion
The original expression [tex]\( 10y + 12 - 7y - 8 - 3y \)[/tex] simplifies to [tex]\( \boxed{4} \)[/tex].
