Let's solve the given linear equation step-by-step.
We start with the equation:
[tex]\[ 2.6(5.5p - 12.4) = 127.92 \][/tex]
### Step 1: Apply the Distributive Property
First, distribute [tex]\( 2.6 \)[/tex] across the terms inside the parentheses:
[tex]\[ 2.6 \cdot 5.5p - 2.6 \cdot 12.4 = 127.92 \][/tex]
Calculate each term:
[tex]\[ 2.6 \cdot 5.5 = 14.3 \][/tex]
[tex]\[ 2.6 \cdot 12.4 = 32.24 \][/tex]
So, substituting these values back into the equation, we get:
[tex]\[ 14.3p - 32.24 = 127.92 \][/tex]
### Step 2: Addition Property of Equality
Next, we need to isolate the term with [tex]\( p \)[/tex] on one side. Add [tex]\( 32.24 \)[/tex] to both sides of the equation:
[tex]\[ 14.3p - 32.24 + 32.24 = 127.92 + 32.24 \][/tex]
Simplify:
[tex]\[ 14.3p = 160.16 \][/tex]
### Step 3: Division Property of Equality
Now, divide both sides by [tex]\( 14.3 \)[/tex] to solve for [tex]\( p \)[/tex]:
[tex]\[ \frac{14.3p}{14.3} = \frac{160.16}{14.3} \][/tex]
[tex]\[ p = \frac{160.16}{14.3} \][/tex]
### Step 4: Calculate the Solution
[tex]\[ p = \frac{160.16}{14.3} \approx 11.2 \][/tex]
So, the solution for [tex]\( p \)[/tex] is:
[tex]\[ \boxed{11.2} \][/tex]
