Question

What is the value of n in the equation
1/2(n-1) - 3 = 3 - (2n + 3)?

Answer 1

`(7)/(5) = n`

Explanation:

`(1)/(2) (n - 1) - 3 = 3 - (2n + 3) \\`

Solve the brackets.

`(n)/(2) - (1)/(2) - 3 = 3 - 2n - 3 \\`

Make the denominator the same to solve the fractions.

`(n)/(2) - (1)/(2) - (3 * 2)/(1 * 2) = 3 - 2n - 3 \\`

Combine like terms.

`(n)/(2) - (1)/(2) - (6)/(2) = - 2n \\ \\ (n - 7)/(2) = - 2n \: \: \: \: \: \: \: \:`

Use cross multiplication to solve for n.

`n - 7 = - 4n \\ \\ - 7 = - 4n - n \\ \\ - 7 = - 5n \: \: \: \: \: \: \\ \\ ( - 7)/( - 5) = ( - 5n)/( - 5) \: \: \: \: \\ \\ (7)/(5) = n \: \: \: \: \: \: \:`

Answer 2

Hey there! :)

1/2(n - 1) - 3 = 3 - (2n + 3)

Simplify.

1/2n - 1/2 - 3 = 3 - 2n - 3

Add like terms.

1/2n - 3 1/2 = -2n

Add 3 1/2 to both sides.

1/2n = -2n + 3 1/2

Then, add 2n to both sides.

1/2n + 2n = 3 1/2

Simplify!

2 1/2n = 3 1/2

Make everything into improper fractions!

5/2n = 7/2

Multiply everything by 2 to get rid of the denominators.

5/2n × 2 = 7/2 × 2

Simplify!

5n = 7

Divide both sides by 5.

n = 7/5

Hope this helped! :)