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Solve this linear equation for [tex]$p$[/tex].

[tex]\[ 2.6(5.5p - 12.4) = 127.92 \][/tex]

1. Distributive property:
[tex]\[ 14.3p - 32.24 = 127.92 \][/tex]

2. Addition property of equality:
[tex]\[ \begin{array}{l}
14.3p - 32.24 + 32.24 = 127.92 + 32.24 \\
14.3p = 160.16
\end{array} \][/tex]

3. Division property of equality:
[tex]\[ \frac{14.3p}{14.3} = \frac{160.16}{14.3} \][/tex]

4. Solution:
[tex]\[ p = \square \][/tex]

Sagot :

GinnyAnswer
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]
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