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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]14.3p - 32.24 + 32.24 = 127.92 + 32.24[/tex]

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

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

Sagot :

GinnyAnswer
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].
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