Answer :
Sure, let's go through the steps one by one for solving the given linear equation \(2.6(5.5p - 12.4) = 127.92\).
1. Distributive property:
[tex]\[ 2.6(5.5p - 12.4) = 2.6 \cdot 5.5p - 2.6 \cdot 12.4 \][/tex]
[tex]\[ 2.6 \cdot 5.5p - 2.6 \cdot 12.4 = 127.92 \][/tex]
[tex]\[ 14.3p - 32.24 = 127.92 \][/tex]
2. Addition property of equality:
[tex]\[ 14.3p - 32.24 + 32.24 = 127.92 + 32.24 \][/tex]
[tex]\[ 14.3p = 160.16 \][/tex]
3. Division property of equality:
[tex]\[ \frac{14.3p}{14.3} = \frac{160.16}{14.3} \][/tex]
[tex]\[ p = \frac{160.16}{14.3} \][/tex]
4. Solution:
[tex]\[ p = 11.2 \][/tex]
So, the solution to the equation [tex]\(2.6(5.5p - 12.4) = 127.92\)[/tex] is [tex]\( p = 11.2 \)[/tex].
1. Distributive property:
[tex]\[ 2.6(5.5p - 12.4) = 2.6 \cdot 5.5p - 2.6 \cdot 12.4 \][/tex]
[tex]\[ 2.6 \cdot 5.5p - 2.6 \cdot 12.4 = 127.92 \][/tex]
[tex]\[ 14.3p - 32.24 = 127.92 \][/tex]
2. Addition property of equality:
[tex]\[ 14.3p - 32.24 + 32.24 = 127.92 + 32.24 \][/tex]
[tex]\[ 14.3p = 160.16 \][/tex]
3. Division property of equality:
[tex]\[ \frac{14.3p}{14.3} = \frac{160.16}{14.3} \][/tex]
[tex]\[ p = \frac{160.16}{14.3} \][/tex]
4. Solution:
[tex]\[ p = 11.2 \][/tex]
So, the solution to the equation [tex]\(2.6(5.5p - 12.4) = 127.92\)[/tex] is [tex]\( p = 11.2 \)[/tex].
