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Answer:
Step-by-step explanation:
|3a|=9
a=3
2- |x–7|=12
For the Negative case we'll use -(x-7)
For the Positive case we'll use (x-7)
Solve the Negative Case
-(x-7) = 12
Multiply
-x+7 = 12
rearrange and Add up
-x = 5
Multiply both sides by (-1)
x = -5 (for negative)
Solve the Positive Case
(x-7) = 12
x = 19
Which is the solution for the Positive Case
Wrap up the solution
x=-5 ,x=19
4- |n+6|=1
The Absolute Value term is |n+6|
For the Negative case we'll use -(n+6)
For the Positive case we'll use (n+6)
Solve the Negative Case
-(n+6) = 1
Multiply
-n-6 = 1
-n = 7
Multiply both sides by (-1)
n = -7
Which is the solution for the Negative Case
Solve the Positive Case
(n+6) = 1
n = -5
Which is the solution for the Positive Case
Wrap up the solution
n=-7
n=-5
5- |1–p|=3
The Absolute Value term is |-p+1|
For the Negative case we'll use -(-p+1)
For the Positive case we'll use (-p+1)
Solve the Negative Case
-(-p+1) = 3
Multiply
p-1 = 3
Rearrange and Add up
p = 4
Solve the Positive Case
(-p+1) = 3
Rearrange and Add up
-p = 2
Multiply both sides by (-1)
p = -2
Which is the solution for the Positive Case
Wrap up the solution
p=4 , p=-2
6 - |6–x|=5
The Absolute Value term is |-x+6|
For the Negative case we'll use -(-x+6)
For the Positive case we'll use (-x+6)
Solve the Negative Case
-(-x+6) = 5
Multiply
x-6 = 5
Rearrange and Add up
x = 11
Solve the Positive Case
(-x+6) = 5
Rearrange and Add up
-x = -1
Multiply both sides by (-1)
x = 1
Which is the solution for the Positive Case
Wrap up the solution
x=11 , x=1
7-
The Absolute Value term is |a+9|
For the Negative case we'll use -(a+9)
For the Positive case we'll use (a+9)
Solve the Negative Case
-(a+9) = 2
Multiply
-a-9 = 2
Rearrange and Add up
-a = 11
Multiply both sides by (-1)
a = -11
Which is the solution for the Negative Case
Solve the Positive Case
(a+9) = 2
Rearrange and Add up a = -7
Which is the solution for the Positive Case
Wrap up the solution
a=-11 a=-7
8- |k–8|=8
The Absolute Value term is |k-8|
For the Negative case we'll use -(k-8)
For the Positive case we'll use (k-8)
Solve the Negative Case
-(k-8) = 8
Multiply
-k+8 = 8
Rearrange and Add up
-k = 0
Multiply both sides by (-1)
k = 0
Which is the solution for the Negative Case
Solve the Positive Case
(k-8) = 8
Rearrange and Add up
k = 16
Which is the solution for the Positive Case
Wrap up the solution
k=0 k=16
Solutions on the Number Line
Two solutions were found :
k=16
k=0
9-|2m+1|=1
The Absolute Value term is |2m+1|
For the Negative case we'll use -(2m+1)
For the Positive case we'll use (2m+1)
Solve the Negative Case
-(2m+1) = 1
Multiply
-2m-1 = 1
Rearrange and Add up
-2m = 2
Divide both sides by 2
-m = 1
Multiply both sides by (-1)
m = -1
Which is the solution for the Negative Case
Solve the Positive Case
(2m+1) = 1
Rearrange and Add up
2m = 0
Divide both sides by 2
m = 0
Which is the solution for the Positive Case
Wrap up the solution
m=-1
m=0
Solutions on the Number Line
Two solutions were found :
m=0
m=-1
9- |7–2r|=5
The Absolute Value term is |-2r+7|
For the Negative case we'll use -(-2r+7)
Solve the Negative Case
-(-2r+7) = 5
Multiply
2r-7 = 5
Rearrange and Add up
2r = 12
Divide both sides by 2
r = 6
Solve the Positive Case
(-2r+7) = 5
Rearrange and Add up
-2r = -2
Divide both sides by 2
-r = -1
Multiply both sides by (-1)
r = 1
Which is the solution for the Positive Case
Wrap up the solution
r=6
r=1
