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Solve this linear equation for [tex][tex]$p$[/tex][/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]
[tex]\[ 14.3p = 160.16 \][/tex]

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

4. Solution:
[tex]\[ p = \boxed{11.2} \][/tex]

Sagot :

GinnyAnswer
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]
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