Let's break down and simplify this expression step-by-step. The given expression is:
[tex]\[ 3.4 - 2.8d + 2.8d - 1.3 \][/tex]
### Step 1: Group like terms
In this expression, we have:
- Constant terms: [tex]\( 3.4 \)[/tex] and [tex]\( -1.3 \)[/tex]
- Variable terms with [tex]\( d \)[/tex]: [tex]\( -2.8d \)[/tex] and [tex]\( 2.8d \)[/tex]
### Step 2: Combine the variable terms
Notice that the variable terms [tex]\( -2.8d \)[/tex] and [tex]\( 2.8d \)[/tex] are like terms, which means they both contain the variable [tex]\( d \)[/tex]:
[tex]\[ -2.8d + 2.8d \][/tex]
These terms sum to zero because:
[tex]\[ -2.8d + 2.8d = 0 \][/tex]
### Step 3: Combine the constant terms
Now, we are left with the constant terms [tex]\( 3.4 \)[/tex] and [tex]\( -1.3 \)[/tex]:
[tex]\[ 3.4 - 1.3 \][/tex]
Subtracting these gives:
[tex]\[ 3.4 - 1.3 = 2.1 \][/tex]
### Step 4: Write the equivalent expression
After combining all the like terms, the equivalent expression is simply the constant term we found:
[tex]\[ 2.1 \][/tex]
### Conclusion
So the simplified and equivalent expression for [tex]\( 3.4 - 2.8d + 2.8d - 1.3 \)[/tex] is:
[tex]\[ \boxed{2.1} \][/tex]
