|3x - 2| + 7 = 15?

|3x - 2| = 8

Case 1: Positive

3x - 2 = 8

3x = 10

x = 10/3

Case 2: Negative

-3x + 2 = 8

-3x = 6

x = -2

~~~~~~~~~~~~~~~

Check solution:

Case 1: x = 10/3

| 3*(10/3) - 2 | + 7 = 15

| 10 -2 | + 7 = 15

8 + 7 = 15

15 = 15 (TRUE)

Case 2: x = -2

| 3(-2) - 2| + 7 = 15

| -6 - 2 | = 8

|-8| = 8

8 = 8 (TRUE)

|3x - 2| + 7 = 15
|3x - 2| = 8

3x - 2 = 8, 3x - 2 = -8
3x = 10, 3x = -6
x = 10/3, x = -2

x = {10/3, -2}

| 3x - 2 | = 8

3x - 2 = 8
3x = 10
x = 10/3

OR

3x - 2 = - 8
3x = - 6
x = - 2

|3x - 2| + 7 = 15
|3x - 2| = 15 - 7
|3x - 2| = 8
3x - 2 = ±8

3x - 2 = 8
3x = 8 + 2
3x = 10
x = 10/3

3x - 2 = -8
3x = -8 + 2
3x = -6
x = -6/3
x = -2

∴ x = 10/3 , -2

(I don't know how to make absolute value bars on my cpu, so the brackets are them for now)

1. subtract 7 from both sides
[3x-2]=8
2. set it up like a regular problem but solve in 2 different ways

3x-2= 8
or
3x-2=-8

3. solve both.

3x=-6
x=-6/3
x=-2

3x=10
x= 10/3

4. the answers are -2 and 10/3

3x + 9 = 15

take away 9 from both sides

3x = 6

divide by 3

x = 2

absolute value equations and inequalities
if b is a positive number
then |p| = b then p = -b or p = b

|p| is |3x-2|+7
b is (+15)
solution
|3x-2|+7 = +-15

(3x - 2 ) + 7 = 15 or (3x-2) + 7 = -15
3x = 15-5 = 10 or 3x - 2 + 7 = -15 -5
x= 10/3 or x = -20/3

remember to check solution by sub it into x value you should get both 15 and -15

cheers.

/3x - 2/ + 7 = 15
/3x - 2/ =8
3x -2 = 8 or 3x -2 = -8
3x = 10 or 3x = -6
x =10/3 or x = -2
Hope that will help you!

(3x-2) +7 = 15
(3x-2) = 15 - 7 = 8
3x = 8 + 2 = 10
x = 10/3 = 3 1/3

-(3x -2) + 7 = 15
- (3x -2) = 15 -7 = 8
- 3x = 8 - 2 =6
3x = -6
x = -2 , 3 1/3