Question Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $12p - 0.7 = 5p + 3.2$ .
2. We need to solve for the variable $p$ .

STEP 2

First, we will collect all terms containing the variable $p$ on one side of the equation and the constant terms on the other side. To do this, we will subtract $5p$ from both sides of the equation.
$12p - 0.7 - 5p = 5p + 3.2 - 5p$

STEP 3

Perform the subtraction on both sides to simplify the equation.
$12p - 5p - 0.7 = 3.2$

STEP 4

Combine like terms on the left side of the equation.
$7p - 0.7 = 3.2$

STEP 5

Next, we will isolate the term with the variable $p$ by adding $0.7$ to both sides of the equation to move the constant term to the right side.
$7p - 0.7 + 0.7 = 3.2 + 0.7$

STEP 6

Perform the addition on both sides to simplify the equation.
$7p = 3.9$

STEP 7

Now, to solve for $p$ , we will divide both sides of the equation by $7$ .
$\frac{7p}{7} = \frac{3.9}{7}$

STEP 8

Perform the division to find the value of $p$ .
$p = \frac{3.9}{7}$

STEP 9

Calculate the value of $p$ .
$p = 0.5571428571...$

STEP 10

If necessary, round the value of $p$ to a desired number of decimal places. For simplicity, we can round to two decimal places.
$p \approx 0.56$
The solution to the equation $12p - 0.7 = 5p + 3.2$ is approximately $p \approx 0.56$ .

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Question Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $12p - 0.7 = 5p + 3.2$ .
2. We need to solve for the variable $p$ .

STEP 2

First, we will collect all terms containing the variable $p$ on one side of the equation and the constant terms on the other side. To do this, we will subtract $5p$ from both sides of the equation.
$12p - 0.7 - 5p = 5p + 3.2 - 5p$

STEP 3

Perform the subtraction on both sides to simplify the equation.
$12p - 5p - 0.7 = 3.2$

STEP 4

Combine like terms on the left side of the equation.
$7p - 0.7 = 3.2$

STEP 5

Next, we will isolate the term with the variable $p$ by adding $0.7$ to both sides of the equation to move the constant term to the right side.
$7p - 0.7 + 0.7 = 3.2 + 0.7$

STEP 6

Perform the addition on both sides to simplify the equation.
$7p = 3.9$

STEP 7

Now, to solve for $p$ , we will divide both sides of the equation by $7$ .
$\frac{7p}{7} = \frac{3.9}{7}$

STEP 8

Perform the division to find the value of $p$ .
$p = \frac{3.9}{7}$

STEP 9

Calculate the value of $p$ .
$p = 0.5571428571...$

STEP 10

If necessary, round the value of $p$ to a desired number of decimal places. For simplicity, we can round to two decimal places.
$p \approx 0.56$
The solution to the equation $12p - 0.7 = 5p + 3.2$ is approximately $p \approx 0.56$ .

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Question Solve the linear equation 12p−0.7=5p+3.212p - 0.7 = 5p + 3.212p−0.7=5p+3.2 for the variable ppp.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 12p−0.7=5p+3.212p - 0.7 = 5p + 3.212p−0.7=5p+3.2.2. We need to solve for the variable ppp.

STEP 2

First, we will collect all terms containing the variable ppp on one side of the equation and the constant terms on the other side. To do this, we will subtract 5p5p5p from both sides of the equation.12p−0.7−5p=5p+3.2−5p12p - 0.7 - 5p = 5p + 3.2 - 5p12p−0.7−5p=5p+3.2−5p

STEP 3

Perform the subtraction on both sides to simplify the equation.12p−5p−0.7=3.212p - 5p - 0.7 = 3.212p−5p−0.7=3.2

STEP 4

Combine like terms on the left side of the equation.7p−0.7=3.27p - 0.7 = 3.27p−0.7=3.2

STEP 5

Next, we will isolate the term with the variable ppp by adding 0.70.70.7 to both sides of the equation to move the constant term to the right side.7p−0.7+0.7=3.2+0.77p - 0.7 + 0.7 = 3.2 + 0.77p−0.7+0.7=3.2+0.7

STEP 6

Perform the addition on both sides to simplify the equation.7p=3.97p = 3.97p=3.9

STEP 7

Now, to solve for ppp, we will divide both sides of the equation by 777.7p7=3.97\frac{7p}{7} = \frac{3.9}{7}77p​=73.9​

STEP 8

Perform the division to find the value of ppp.p=3.97p = \frac{3.9}{7}p=73.9​

STEP 9

Calculate the value of ppp.p=0.5571428571...p = 0.5571428571...p=0.5571428571...

STEP 10

If necessary, round the value of ppp to a desired number of decimal places. For simplicity, we can round to two decimal places.p≈0.56p \approx 0.56p≈0.56The solution to the equation 12p−0.7=5p+3.212p - 0.7 = 5p + 3.212p−0.7=5p+3.2 is approximately p≈0.56p \approx 0.56p≈0.56.

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Question Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

Assumptions
1. We are given the equation $12p - 0.7 = 5p + 3.2$ .
2. We need to solve for the variable $p$ .

First, we will collect all terms containing the variable $p$ on one side of the equation and the constant terms on the other side. To do this, we will subtract $5p$ from both sides of the equation.
$12p - 0.7 - 5p = 5p + 3.2 - 5p$

Perform the subtraction on both sides to simplify the equation.
$12p - 5p - 0.7 = 3.2$

Combine like terms on the left side of the equation.
$7p - 0.7 = 3.2$

Next, we will isolate the term with the variable $p$ by adding $0.7$ to both sides of the equation to move the constant term to the right side.
$7p - 0.7 + 0.7 = 3.2 + 0.7$

Perform the addition on both sides to simplify the equation.
$7p = 3.9$

Now, to solve for $p$ , we will divide both sides of the equation by $7$ .
$\frac{7p}{7} = \frac{3.9}{7}$

Perform the division to find the value of $p$ .
$p = \frac{3.9}{7}$

Calculate the value of $p$ .
$p = 0.5571428571...$

If necessary, round the value of $p$ to a desired number of decimal places. For simplicity, we can round to two decimal places.
$p \approx 0.56$
The solution to the equation $12p - 0.7 = 5p + 3.2$ is approximately $p \approx 0.56$ .