5(2+n) = 3(n+6)

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william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

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To solve this equation, first open the brackets, we get:

5*( 2+n ) = 3*( n+6)

=> 5*2+ 5*n = 3*n+ 3*6

=> 10 +5n =3n +18

Take the numbers and the terms with n to opposite sides of the equation:

=> 5n - 3n = 18 - 10

=> 2n = 8

Divide both sides by 2

=> n = 4

Therefore n=4

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

5(2+n) = 3(n+6)

To solve for n.

Solution:

5(2+n) =3(n+6) is a linear equation of one variable n.

To solve forn we collect n at one side and the numbers or values on the pther side by operations of adding or subtracting equals. And the multiplying or dividing by equals (but not by zero).

OPen the brakets :

5*2 +5n = 3n+3*6

10+5n = 3n+18.

Subtract 3n:

10+5n-3n = 18

10+2n =3n+18.

Subtract 10:

2n = 18-10

2n = 8

Divide by 2:

n = 8/2 = 4.

n = 4.

Tally.

Put n= 4 in the given equation 5(2+n) = 3(n+6)

LHS=5(2+40n) = 5(2+4) = 5*6 = 30

RHS =3(4+6) = 3*10 = 30.

So for n =4, the equation is satisfied.

 

 

 

 4

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

In order to to solve the equation and to find the value of n for the identity to be tru, we'll follow the steps:

- First, we'll remove the brackets, both sides:

5(2+n) = 3(n+6)

10 + 5n = 3n + 18

- Now, we'll isolate the terms that contain "n", to the left side. For this reason, we'll subtract 3n both sides:

10 + 5n - 3n = 3n - 3n + 18

We'll reduce like terms and we'll get:

10 + 2n = 0 + 18

 - Now, we'll subtract 10 both sides:

10 + 2n - 10 = 18 - 10

We'll reduce like terms and we'll get:

2n = 8

We'll divide by 2, both sides:

n = 8/2

n = 4

So, the solution of the given equation is n = 4.

- To verify the equation, we'll input the value 4 in the given expression:

5(2+4) = 3(4+6)

We'll calculate the sum in each pair of brackets:

5 * 6 = 3 * 10

30 = 30

The identity is verified for n = 4, so the solution n = 4 is valid.

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

This problem will require distribution

5(2+n) = 3(n+6)

10+5n=3n+18

Move all the variables on one side

5n-3n=18-10

2n=8

Divide by 2

n=4

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

5 ( 2 + n ) = 3 ( n + 6 )

First distribute the 5 and the 3. By doing that, your equation should look like

10 + 5n = 3n + 18 Now, subtract 3n from both sides, this way all the " n " would be on the same side making it easier to solve

By subtracting 3n from both sides the equation would be

10 + 2n = 18 Now subtract 10 from both sides

By subtracting 10 from both sides your equation should be

2n = 8 Divide 2 from both sides

By dividing your equation should look like

n = 4 which is your answer

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