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**

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

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.**

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

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