Question

4n=1/2(2n-12) check the solution to the example problem by replacing n in the original equation with -2 and evaluating both sides. What true statement do you get?

Answer 1

The true statement is that the expression is satisfied for n = -2.

Explanation:

Given:

`4n = (1)/(2)* (2n-12)`

To check:

Left hand side = Right-hand side ( for n = -2)

Proof :

For n = -2

Consider Left hand side of the equation given above.

∴ Left hand side = 4n

= 4×(-2) ......................for n = -2

= -8

Consider Right-hand side of the equation given above

∴ Right-hand side =
`(1)/(2)* (2n-12)`

`=(1)/(2)* (2*(-2) - 12) \\= (1)/(2)* (-4 - 12)\\ =(1)/(2)* (-16)\\ =-8`

Now we get Left hand side equal to Right hand side

i.e. Left hand side = Right hand side

i.e.
`4n = (1)/(2)* (2n-12)` is true for n = -2