Sure, let's solve the linear equation step-by-step.
Given equation:
[tex]\[ 2.6(5.5p - 12.4) = 127.92 \][/tex]
Step 1: Distributive Property
Apply the distributive property to the left-hand side:
[tex]\[ 2.6 \times 5.5p - 2.6 \times 12.4 \][/tex]
Calculating each term individually:
[tex]\[ 2.6 \times 5.5 = 14.3 \][/tex]
[tex]\[ 2.6 \times 12.4 = 32.24 \][/tex]
So, the equation becomes:
[tex]\[ 14.3p - 32.24 = 127.92 \][/tex]
Step 2: Addition Property of Equality
Add 32.24 to both sides of the equation to isolate the term with [tex]\( p \)[/tex]:
[tex]\[ 14.3p - 32.24 + 32.24 = 127.92 + 32.24 \][/tex]
Simplifying both sides:
[tex]\[ 14.3p = 160.16 \][/tex]
Step 3: Division Property of Equality
Divide both sides by 14.3 to solve for [tex]\( p \)[/tex]:
[tex]\[ \frac{14.3p}{14.3} = \frac{160.16}{14.3} \][/tex]
Simplifying the division on the right-hand side:
[tex]\[ p = 11.2 \][/tex]
Solution
Thus, the value of [tex]\( p \)[/tex] is:
[tex]\[ p = 11.2 \][/tex]
