Solve 2(n-5)+3n-1=2(n+3)-(n+1)

$$2 ( n - 5 ) + 3 n - 1 = 2 ( n + 3 ) - ( n + 1 )$$

Solve for n

$$n=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by n-5.

$$2n-10+3n-1=2\left(n+3\right)-\left(n+1\right)$$

Combine 2n and 3n to get 5n.

$$5n-10-1=2\left(n+3\right)-\left(n+1\right)$$

Subtract 1 from -10 to get -11.

$$5n-11=2\left(n+3\right)-\left(n+1\right)$$

Use the distributive property to multiply 2 by n+3.

$$5n-11=2n+6-\left(n+1\right)$$

To find the opposite of n+1, find the opposite of each term.

$$5n-11=2n+6-n-1$$

Combine 2n and -n to get n.

$$5n-11=n+6-1$$

Subtract 1 from 6 to get 5.

$$5n-11=n+5$$

Subtract n from both sides.

$$5n-11-n=5$$

Combine 5n and -n to get 4n.

$$4n-11=5$$

Add 11 to both sides.

$$4n=5+11$$

Add 5 and 11 to get 16.

$$4n=16$$

Divide both sides by 4.

$$n=\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$n=4$$