Question

What is the value of n in the equation 1 (n – 4) – 3 = 3 - (2n+3)?

Answer 1

Explanation:

`1(n-4)-3=3-(2n+3)`

`n-4-3=3-2n-3\\n+2n=3-3+3+4\\3n=7\\n=(7)/(3)`

Proof

`1(n-4)-3=3-(2n+3)`

`1((7)/(3) -4)-3=3-[2((7)/(3)) +3]\\1((7-12)/(3) )-3=3-((14)/(3) +3)\\1((-5)/(3) )-3=3-((14+9)/(3))\\(-5)/(3) -3=3-((23)/(3))`

`(-5-9)/(3) =(9-23)/(3) \\(-14)/(3) =(-14)/(3)`

Answer 2

n=7/3

Explanation:

1 (n – 4) – 3 = 3 - (2n+3)

1. distribute the 1 on the left side and distribute the -1 on the right side

1n-4-3=3-2n-3

2. add like terms

1n-7=-2n

3. move n to one side and by itself

-7=-3n

4. divide -3 to get n alone. Both negatives cancel out each other

7/3=n