Question

Solve the equation

1/2 k + 2 = 5 + 5/6 k

a. 2 1/4
b. -9
c. 9
d. -21

Please select the best answer from the choices provided​

Answer 1

1/2k+2=5+5/6k

-3 = 5/6k-1/2k

-3=2/6k

k= -9

Answer 2

Final Answer:
`k = -9`

Steps/Reasons/Explanation:

Question: Solve the equation
`(1)/(2) k + 2 = 5 + (5)/(6)k`. Please select the best answer from the choices provided​.

`a.`
`2(1)/(4)`

`b.`
`-9`

`c.`
`9`

`d.`
`-21`

Step 1: Simplify
`(1)/(2)k` to
`(k)/(2)`.

`(k)/(2) + 2 = 5 + (5)/(6)k`

Step 2: Simplify
`(5)/(6)k` to
`(5k)/(6)`.

`(k)/(2) + 2 = 5 + (5k)/(6)`

Step 3: Multiply both sides by
`6` (the LCM of
`2, 6`).

`3k + 12 = 30 + 5k`

Step 4: Subtract
`3k` from both sides.

`12 = 30 + 5k - 3k`

Step 5: Simplify
`30 + 5k - 3k` to
`30 + 2k`.

`12 = 30 + 2k`

Step 6: Subtract
`30` from both sides.

`12 - 30 = 2k`

Step 7: Simplify
`12 - 30` to
`-18`.

`-18 = 2k`

Step 8: Divide both sides by
`2`.

`-(18)/(2) = k`

Step 9: Simplify
`-(18)/(2)` to
`-9`.

`-9 = k`

Step 10: Switch sides.

`k = -9`

~I hope I helped you :)~