how can I solve 1/5 (2a - 5) - 4 = 1/2 (a + 4) - 7/16?

1/5(2a - 5) - 4 = 1/2(a + 4) - 7/16
(2a - 5)/5 - 4 = (a + 4)/2 - 7/16
80[(2a - 5)/5 - 4] = 80[(a + 4)/2 - 7/16]
16(2a - 5) - 80(4) = 40(a + 4) - 5(7)
16*2a - 16*5 - 320 = 40*a + 40*4 - 35
32a - 80 - 320 = 40a + 160 - 35
32a - 400 = 40a + 125
32a - 40a = 400 + 125
-8a = 525
a = 525/-8
a = -525/8 (-65.625)

16 (2a - 5) - 320 = 40 (a + 4) - 35
32a - 80 - 320 = 40a + 160 - 35
- 400 - 160 + 35 = 8a
- 525 = 8a
a = - 525 / 8

distribute first

(2/5a) -1 - 4 =(1/2a) + 2 - 7/16 Combine like terms
2/5a - 5 = 1/2a + 25/16 isolate A
+5 +5

2/5a = 1/2a + 105/16
-1/2a -1/2a

2 1
---a - ---a= 105/16
5 2

4 5
---a - ------a= 105/16
10 10

- 1
----a = 105/16
10

a= 65.625

multiply it by 10...

2a - 5 - 40 = 5a + 20 - 35/8

combining similar terms...

5a - 2a = 35/8 -5 - 40 - 20
3a = 35/8 - 65
3a = (35 - 520)/8
3a = -485/8
a = -485/24
a = -20 5/24 is the answer!

let's see if I get the same answer

1/5 (2a - 5) - 4 = 1/2 (a + 4) - 7/16

re-organize the fraction

(2a - 5) / 5 - 4 = (a + 4) / 2 - 7/16

get a common denominator on each side

(2a - 5) / 5 - (4 * 5) / 5 = ((a + 4) * 8) / 16 - 7/16
(2a -5 - 20 ) / 5 = (8a +32 - 7 ) / 16
(2a - 25) / 5 = (8a + 25 ) / 16

get a common denominator for both sides now... let's say 80

((2a -25) * 16) / (5 * 16) = ((8a + 25) * 5) / (16 * 5)

(32a - 400) / 80 = (40a + 125) / 80

multiply both sides by 80 to remove the fraction

32a - 400 = 40a + 125

subtract 32a from both sides

-400 = 8a + 125

subtract 125 from both sides

-525 = 8a

divide both sides by 8

a = -525/8

a = -65.625

or... turn it into a compound fraction

a = -( 65 5/8 )