To solve the linear equation \(2.6(5.5p - 12.4) = 127.92\), follow these steps:
### Step 1: Apply the Distributive Property
First, distribute the 2.6 to both terms inside the parentheses:
[tex]\[2.6 \times 5.5p - 2.6 \times 12.4 = 127.92\][/tex]
Calculate the multiplications:
[tex]\[14.3p - 32.24 = 127.92\][/tex]
### Step 2: Use the Addition Property of Equality
Next, isolate the term containing \(p\) by adding 32.24 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: Use the Division Property of Equality
Finally, solve for \(p\) by dividing both sides of the equation by 14.3:
[tex]\[\frac{14.3p}{14.3} = \frac{160.16}{14.3}\][/tex]
Simplify:
[tex]\[p = 11.2\][/tex]
### Solution
[tex]\[p = 11.2\][/tex]