Solved on Mar 05, 2024

Solve for $p$ in the linear equation $2.6(5.5p-12.4)=127.92$ . Use distributive, addition, and division properties to find $p=\frac{160.16}{14.3}$ .

STEP 1

Assumptions
1. We are given a linear equation in the form $2.6(5.5p - 12.4) = 127.92$ .
2. We need to solve for the variable $p$ .
3. We will use the distributive property to expand the equation.
4. We will use the addition property of equality to isolate the variable term.
5. We will use the division property of equality to solve for $p$ .

STEP 2

First, we will apply the distributive property to remove the parentheses by multiplying $2.6$ with both $5.5p$ and $-12.4$ .
$2.6(5.5p) - 2.6(12.4) = 127.92$

STEP 3

Now, we perform the multiplication to simplify the left-hand side of the equation.
$14.3p - 32.24 = 127.92$

STEP 4

Next, we will use the addition property of equality to move the constant term on the left-hand side to the right-hand side. We do this by adding $32.24$ to both sides of the equation.
$14.3p - 32.24 + 32.24 = 127.92 + 32.24$

STEP 5

Simplify both sides of the equation by combining like terms.
$14.3p = 160.16$

STEP 6

Now, we will apply the division property of equality to solve for $p$ by dividing both sides of the equation by $14.3$ .
$\frac{14.3p}{14.3} = \frac{160.16}{14.3}$

STEP 7

Perform the division to find the value of $p$ .
$p = \frac{160.16}{14.3}$

STEP 8

Calculate the value of $p$ .
$p = 11.2$

STEP 9

Solution
The solution to the equation $2.6(5.5p - 12.4) = 127.92$ is $p = 11.2$ .

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Solve for $p$ in the linear equation $2.6(5.5p-12.4)=127.92$ . Use distributive, addition, and division properties to find $p=\frac{160.16}{14.3}$ .

STEP 1

STEP 2

First, we will apply the distributive property to remove the parentheses by multiplying $2.6$ with both $5.5p$ and $-12.4$ .
$2.6(5.5p) - 2.6(12.4) = 127.92$

STEP 3

Now, we perform the multiplication to simplify the left-hand side of the equation.
$14.3p - 32.24 = 127.92$

STEP 4

Next, we will use the addition property of equality to move the constant term on the left-hand side to the right-hand side. We do this by adding $32.24$ to both sides of the equation.
$14.3p - 32.24 + 32.24 = 127.92 + 32.24$

STEP 5

Simplify both sides of the equation by combining like terms.
$14.3p = 160.16$

STEP 6

Now, we will apply the division property of equality to solve for $p$ by dividing both sides of the equation by $14.3$ .
$\frac{14.3p}{14.3} = \frac{160.16}{14.3}$

STEP 7

Perform the division to find the value of $p$ .
$p = \frac{160.16}{14.3}$

STEP 8

Calculate the value of $p$ .
$p = 11.2$

STEP 9

Solution
The solution to the equation $2.6(5.5p - 12.4) = 127.92$ is $p = 11.2$ .

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Solve for ppp in the linear equation 2.6(5.5p−12.4)=127.922.6(5.5p-12.4)=127.922.6(5.5p−12.4)=127.92. Use distributive, addition, and division properties to find p=160.1614.3p=\frac{160.16}{14.3}p=14.3160.16​.

STEP 1

STEP 2

First, we will apply the distributive property to remove the parentheses by multiplying 2.62.62.6 with both 5.5p5.5p5.5p and −12.4-12.4−12.4.2.6(5.5p)−2.6(12.4)=127.922.6(5.5p) - 2.6(12.4) = 127.922.6(5.5p)−2.6(12.4)=127.92

STEP 3

Now, we perform the multiplication to simplify the left-hand side of the equation.14.3p−32.24=127.9214.3p - 32.24 = 127.9214.3p−32.24=127.92

STEP 4

Next, we will use the addition property of equality to move the constant term on the left-hand side to the right-hand side. We do this by adding 32.2432.2432.24 to both sides of the equation.14.3p−32.24+32.24=127.92+32.2414.3p - 32.24 + 32.24 = 127.92 + 32.2414.3p−32.24+32.24=127.92+32.24

STEP 5

Simplify both sides of the equation by combining like terms.14.3p=160.1614.3p = 160.1614.3p=160.16

STEP 6

Now, we will apply the division property of equality to solve for ppp by dividing both sides of the equation by 14.314.314.3.14.3p14.3=160.1614.3\frac{14.3p}{14.3} = \frac{160.16}{14.3}14.314.3p​=14.3160.16​

STEP 7

Perform the division to find the value of ppp.p=160.1614.3p = \frac{160.16}{14.3}p=14.3160.16​

STEP 8

Calculate the value of ppp.p=11.2p = 11.2p=11.2

STEP 9

SolutionThe solution to the equation 2.6(5.5p−12.4)=127.922.6(5.5p - 12.4) = 127.922.6(5.5p−12.4)=127.92 is p=11.2p = 11.2p=11.2.

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Solve for $p$ in the linear equation $2.6(5.5p-12.4)=127.92$ . Use distributive, addition, and division properties to find $p=\frac{160.16}{14.3}$ .

First, we will apply the distributive property to remove the parentheses by multiplying $2.6$ with both $5.5p$ and $-12.4$ .
$2.6(5.5p) - 2.6(12.4) = 127.92$

Now, we perform the multiplication to simplify the left-hand side of the equation.
$14.3p - 32.24 = 127.92$

Next, we will use the addition property of equality to move the constant term on the left-hand side to the right-hand side. We do this by adding $32.24$ to both sides of the equation.
$14.3p - 32.24 + 32.24 = 127.92 + 32.24$

Simplify both sides of the equation by combining like terms.
$14.3p = 160.16$

Now, we will apply the division property of equality to solve for $p$ by dividing both sides of the equation by $14.3$ .
$\frac{14.3p}{14.3} = \frac{160.16}{14.3}$

Perform the division to find the value of $p$ .
$p = \frac{160.16}{14.3}$

Calculate the value of $p$ .
$p = 11.2$

Solution
The solution to the equation $2.6(5.5p - 12.4) = 127.92$ is $p = 11.2$ .