What is the solution set for the given equation? 3|x + 4| = 18

Let's try a different approach this time...

3|x + 4| = 18

has the same solution as

|x + 4| = 6


We look for the number(s) that can add/subtract to obtain 6. We can see that x=2 will work. No other positive number will work, however if we consider negative numbers then -10 seems possible. In fact is does work because |-10+4| = |-6| = 6. So x=-10.

Find the solution set for the absolute value equation.

Find the solution set for the equation.

|x  - 7| = | 8 - x|

|x  - 7| = | 8 - x| 

means

x  - 7 =  8 - x  or   x - 7 = -8 + x (which has no solution)

we we can write

x + x - 7 - 8 = -x + x

2x -15 = 0

2x = 15

x = 15/2

Solve: 8|2-9p|-2=14

8|2-9p|-2=14
8|2-9p|-2+2=14+2
8|2-9p|=16
8/8|2-9p|=16/8
|2-9p|=2 

case 1)
2-9p=2
-9p=0
p=0 

case 2)
2-9p=-2
-9p=-4
p=4/9

Explain why solving an equation containing one absolute value expression does not apply to the expression | x - 5 | = -3?

One useful and naturally intuitive definition is that the absolute value of an number is it's distance from 0 on the number line. If we use this definition then we require that the absolute value of a real valued quantity be greater than or equal to zero. We also know that both sides of any equation must have the same sign to have a solution- therefore this equation is a contradiction.

Please solve |x^2+3x|=|x^2-2x|

removing the absolute vale leads to
case 1:
 or
case 2:


case 1:





case 2:


 or 

solutions: {0, -1/2}

Solve: |3x-1|=4x

|3x-1|=4x 
3x-1=4x or 3x-1=-4x 
x=-1 or x=1/7 
but x=-1 is impossible, so 
x=1/7

for what values of c does |2x+1|= x+c have two solutions?

Solving this problem by analyzing the graphs is the easiest way I can think of...
y=|2x+1|
y=x+c
these two graphs will not intersect for any value of c < 1/2 and at c=1/2 there is only 1 intersection. So we can see that the graphs will intersect at exactly two points for any value of c > 1/2

Solve: |2a-4|=-2a+4

it means the same as:
2a-4=-2a+4 or 2a-4=-(-2a+4)
4a=8 or 0=0
a=2
but notice that the expressions 2a-4 and -2a+4 have the same value when

so that is our solution

Solve: |2p-3|=17

means the same as:
2p-3=17 or 2p-3=-17
2p=20 or 2p=-14
p=10 or p=-7

Solve: |4x+7|+5>4

|4x+7|+5-5>4-5

|4x+7|>-1
which is true for all real numbers

|2r - 1| = 1/4. The answer was 3/8 and 5/8. We could figure out the 5/8 but how do you get 3/8?

it means:
2r-1=1/4
or
2r-1=-1/4 which leads to
2r=-1/4+1
2r=3/4
r=3/8

Solve for x: 3-|8x-6|=3

3-|8x-6|=3
|8x-6|=0
8x-6=0
x=3/4

Solve the absolute value equation: ||2x+1|-18|=4

The easiest way to solve any absolute value problem is to determine all possible equations with respect to the signs of the expressions. This equation has 4 possibilities: 


case 1)
2x+1-18=4 
2x=21
x=21/2 

case 2)
-2x-1-18=4
-2x=23
x=-23/2 


case 3)
2x+1-18=-4
2x=13
x=13/2 

case 4)
-2x-1 -18=-4
-2x=15
x=-15/2