Question

Given that a♥b =
2
a
(
3
2
− b)

If a♥b = −
2
3
, solve for b in terms of a.
A) b =
1
6
a +
3
2
B) b =
1
3
a +
3
2
C) b =
1
2
a +
3
2
D) b =
1
6
a −
3
2
PLEASE HELP ME I NEED HELP 

Answer 1

First of all, write these in a way people can read them in the future. Don't make it so hard to help you.

Secondly:

Given that a♥b = 2a(32− b)

If a♥b = −23, solve for b in terms of a.

A) b = 16a + 32
B) b = 13a + 32
C) b = 12a + 32
D) b = 16a − 32

-23 = 2a(32− b),  devide both sides by 2a -23/2a = 32 - b, subtract 32 from both sides -23/2a - 32 = -b, multiply both sides by -1  23/2a + 32 = b

verified:
b = 23/2a + 32 
-23 = 2a(32 − (23/2a + 32))
-23 = 2a(32 -23/2a -32)
-23 = 2a(-23/2a)
-23 = -23

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