Solved on Feb 07, 2024

Find the value of $n$ when $8n - 2 = 6n + 6$ .

STEP 1

Assumptions
1. The equation to solve is $8n - 2 = 6n + 6$ .
2. We are solving for the variable $n$ .

STEP 2

First, we want to collect all the terms with $n$ on one side of the equation and the constant terms on the other side. We can do this by subtracting $6n$ from both sides of the equation.
$8n - 2 - 6n = 6n + 6 - 6n$

STEP 3

Simplify both sides of the equation by combining like terms.
$2n - 2 = 6$

STEP 4

Next, we want to isolate $n$ by getting rid of the constant term on the left side. We can do this by adding 2 to both sides of the equation.
$2n - 2 + 2 = 6 + 2$

STEP 5

Simplify both sides of the equation.
$2n = 8$

STEP 6

Now, to solve for $n$ , we divide both sides of the equation by 2.
$\frac{2n}{2} = \frac{8}{2}$

STEP 7

Simplify both sides of the equation to find the value of $n$ .
$n = 4$
The value of $n$ is 4.

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Find the value of $n$ when $8n - 2 = 6n + 6$ .

STEP 1

Assumptions
1. The equation to solve is $8n - 2 = 6n + 6$ .
2. We are solving for the variable $n$ .

STEP 2

First, we want to collect all the terms with $n$ on one side of the equation and the constant terms on the other side. We can do this by subtracting $6n$ from both sides of the equation.
$8n - 2 - 6n = 6n + 6 - 6n$

STEP 3

Simplify both sides of the equation by combining like terms.
$2n - 2 = 6$

STEP 4

Next, we want to isolate $n$ by getting rid of the constant term on the left side. We can do this by adding 2 to both sides of the equation.
$2n - 2 + 2 = 6 + 2$

STEP 5

Simplify both sides of the equation.
$2n = 8$

STEP 6

Now, to solve for $n$ , we divide both sides of the equation by 2.
$\frac{2n}{2} = \frac{8}{2}$

STEP 7

Simplify both sides of the equation to find the value of $n$ .
$n = 4$
The value of $n$ is 4.

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Find the value of nnn when 8n−2=6n+68n - 2 = 6n + 68n−2=6n+6.

STEP 1

Assumptions1. The equation to solve is 8n−2=6n+68n - 2 = 6n + 68n−2=6n+6.2. We are solving for the variable nnn.

STEP 2

First, we want to collect all the terms with nnn on one side of the equation and the constant terms on the other side. We can do this by subtracting 6n6n6n from both sides of the equation.8n−2−6n=6n+6−6n8n - 2 - 6n = 6n + 6 - 6n8n−2−6n=6n+6−6n

STEP 3

Simplify both sides of the equation by combining like terms.2n−2=62n - 2 = 62n−2=6

STEP 4

Next, we want to isolate nnn by getting rid of the constant term on the left side. We can do this by adding 2 to both sides of the equation.2n−2+2=6+22n - 2 + 2 = 6 + 22n−2+2=6+2

STEP 5

Simplify both sides of the equation.2n=82n = 82n=8

STEP 6

Now, to solve for nnn, we divide both sides of the equation by 2.2n2=82\frac{2n}{2} = \frac{8}{2}22n​=28​

STEP 7

Simplify both sides of the equation to find the value of nnn.n=4n = 4n=4The value of nnn is 4.

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Find the value of $n$ when $8n - 2 = 6n + 6$ .

Assumptions
1. The equation to solve is $8n - 2 = 6n + 6$ .
2. We are solving for the variable $n$ .

First, we want to collect all the terms with $n$ on one side of the equation and the constant terms on the other side. We can do this by subtracting $6n$ from both sides of the equation.
$8n - 2 - 6n = 6n + 6 - 6n$

Simplify both sides of the equation by combining like terms.
$2n - 2 = 6$

Next, we want to isolate $n$ by getting rid of the constant term on the left side. We can do this by adding 2 to both sides of the equation.
$2n - 2 + 2 = 6 + 2$

Simplify both sides of the equation.
$2n = 8$

Now, to solve for $n$ , we divide both sides of the equation by 2.
$\frac{2n}{2} = \frac{8}{2}$

Simplify both sides of the equation to find the value of $n$ .
$n = 4$
The value of $n$ is 4.