Question

This is an absolute value equation I am a bit confused with
4 I 3a+4 I = 16a+8 between 4 and 3 and again between 4 and= and the absolute value signs.

Answer 1

the absolute signs means the absolute value of 3a + 4 - that means the positive value only so that if the value of 3a + 4 is negative it takes on the positive value.

so for example if a = -10 making 3a+4 = -26 - its abso;ute value is positive 26

Answer 2

4 I 3a+4 I = 16a+8 is the complete equation

Answer 3

4 I 3a+4 I = 16a+8
divide both sides by 4
I 3a+4 I = 4a + 2
take positive value :
3a + 4 = 4a + 2
a = 2 is one solution

take negative value:

3a + 4 = -(4a + 2)
3a + 4 = -4a - 2
7a = -6
a = -6/7 is other solution

Answer 4

4 I 3a+4 I = 16a+8
divide both sides by 4 I 3a+4 I = 4a + 2
take positive value :
3a + 4 = 4a + 2...........I subtracted 4 from both sides to Isolate the left 3a
so I end up with 4a -2
then after dividing both sides by 4a i arrive at a = -2

a = 2 is one solution

Answer 5

The second negative - answer I came up as you did.