Solved on Jan 22, 2024

Solve the linear equation $9 = 5n + 6 - 6n$ for the value of $n$ .

STEP 1

Assumptions
1. The equation to solve is $9 = 5n + 6 - 6n$ .
2. We need to find the value of $n$ .

STEP 2

First, we will combine like terms on the right side of the equation.
$5n - 6n + 6$

STEP 3

Subtract $6n$ from $5n$ to simplify the right side of the equation.
$5n - 6n = -n$

STEP 4

Now, rewrite the equation with the simplified term.
$9 = -n + 6$

STEP 5

Next, we need to isolate the variable $n$ on one side of the equation. We will do this by subtracting $6$ from both sides of the equation.
$9 - 6 = -n + 6 - 6$

STEP 6

Perform the subtraction on both sides of the equation.
$3 = -n$

STEP 7

To solve for $n$ , we need to get rid of the negative sign in front of $n$ . We can do this by multiplying both sides of the equation by $-1$ .
$-1 \times 3 = -1 \times (-n)$

STEP 8

Multiply both sides by $-1$ to find the value of $n$ .
$-3 = n$
The solution to the equation $9 = 5n + 6 - 6n$ is $n = -3$ .

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Solve the linear equation $9 = 5n + 6 - 6n$ for the value of $n$ .

STEP 1

Assumptions
1. The equation to solve is $9 = 5n + 6 - 6n$ .
2. We need to find the value of $n$ .

STEP 2

First, we will combine like terms on the right side of the equation.
$5n - 6n + 6$

STEP 3

Subtract $6n$ from $5n$ to simplify the right side of the equation.
$5n - 6n = -n$

STEP 4

Now, rewrite the equation with the simplified term.
$9 = -n + 6$

STEP 5

Next, we need to isolate the variable $n$ on one side of the equation. We will do this by subtracting $6$ from both sides of the equation.
$9 - 6 = -n + 6 - 6$

STEP 6

Perform the subtraction on both sides of the equation.
$3 = -n$

STEP 7

To solve for $n$ , we need to get rid of the negative sign in front of $n$ . We can do this by multiplying both sides of the equation by $-1$ .
$-1 \times 3 = -1 \times (-n)$

STEP 8

Multiply both sides by $-1$ to find the value of $n$ .
$-3 = n$
The solution to the equation $9 = 5n + 6 - 6n$ is $n = -3$ .

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Solve the linear equation 9=5n+6−6n9 = 5n + 6 - 6n9=5n+6−6n for the value of nnn.

STEP 1

Assumptions1. The equation to solve is 9=5n+6−6n9 = 5n + 6 - 6n9=5n+6−6n.2. We need to find the value of nnn.

STEP 2

First, we will combine like terms on the right side of the equation.5n−6n+65n - 6n + 65n−6n+6

STEP 3

Subtract 6n6n6n from 5n5n5n to simplify the right side of the equation.5n−6n=−n5n - 6n = -n5n−6n=−n

STEP 4

Now, rewrite the equation with the simplified term.9=−n+69 = -n + 69=−n+6

STEP 5

Next, we need to isolate the variable nnn on one side of the equation. We will do this by subtracting 666 from both sides of the equation.9−6=−n+6−69 - 6 = -n + 6 - 69−6=−n+6−6

STEP 6

Perform the subtraction on both sides of the equation.3=−n3 = -n3=−n

STEP 7

To solve for nnn, we need to get rid of the negative sign in front of nnn. We can do this by multiplying both sides of the equation by −1-1−1.−1×3=−1×(−n)-1 \times 3 = -1 \times (-n)−1×3=−1×(−n)

STEP 8

Multiply both sides by −1-1−1 to find the value of nnn.−3=n-3 = n−3=nThe solution to the equation 9=5n+6−6n9 = 5n + 6 - 6n9=5n+6−6n is n=−3n = -3n=−3.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the linear equation $9 = 5n + 6 - 6n$ for the value of $n$ .

Assumptions
1. The equation to solve is $9 = 5n + 6 - 6n$ .
2. We need to find the value of $n$ .

First, we will combine like terms on the right side of the equation.
$5n - 6n + 6$

Subtract $6n$ from $5n$ to simplify the right side of the equation.
$5n - 6n = -n$

Now, rewrite the equation with the simplified term.
$9 = -n + 6$

Next, we need to isolate the variable $n$ on one side of the equation. We will do this by subtracting $6$ from both sides of the equation.
$9 - 6 = -n + 6 - 6$

Perform the subtraction on both sides of the equation.
$3 = -n$

To solve for $n$ , we need to get rid of the negative sign in front of $n$ . We can do this by multiplying both sides of the equation by $-1$ .
$-1 \times 3 = -1 \times (-n)$

Multiply both sides by $-1$ to find the value of $n$ .
$-3 = n$
The solution to the equation $9 = 5n + 6 - 6n$ is $n = -3$ .