Math

Question Solve the linear equation 3(n9)2(n+4)=6n3(n-9)-2(n+4)=6n for the value of nn.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 3(n9)2(n+4)=6n3(n-9)-2(n+4)=6n.
2. We need to solve for the variable nn.

STEP 2

Distribute the multiplication over addition and subtraction in the left-hand side of the equation.
3(n9)2(n+4)=3n392n243(n-9)-2(n+4) = 3n - 3 \cdot 9 - 2n - 2 \cdot 4

STEP 3

Perform the multiplication.
3n272n83n - 27 - 2n - 8

STEP 4

Combine like terms on the left-hand side of the equation.
(3n2n)(27+8)(3n - 2n) - (27 + 8)

STEP 5

Simplify the terms.
n35n - 35

STEP 6

Rewrite the equation with the simplified left-hand side.
n35=6nn - 35 = 6n

STEP 7

Move all terms containing nn to one side of the equation and constants to the other side. We can do this by adding 3535 to both sides and subtracting 6n6n from both sides.
n6n=35n - 6n = 35

STEP 8

Combine like terms.
5n=35-5n = 35

STEP 9

Divide both sides by 5-5 to isolate nn.
5n5=355\frac{-5n}{-5} = \frac{35}{-5}

STEP 10

Solve for nn.
n=7n = -7
The solution to the equation is n=7n = -7.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord