# data[].attributes.body
In this lesson you will learn:

Solve absolute value inequalities in one variable. 
Graph the solution to an absolute value inequality on a number line. 
Solve and graph absolute value inequalities in real world contexts. 

# data[].attributes.body
In this lesson you will learn:

Solve absolute value inequalities in one variable. 
Graph the solution to an absolute value inequality on a number line. 
Solve and graph absolute value inequalities in real world contexts. 

# data[].attributes.body
In this lesson you will learn:

Solve absolute value inequalities in one variable. 
Graph the solution to an absolute value inequality on a number line. 
Solve and graph absolute value inequalities in real world contexts. 

# data[].attributes.body
In this lesson you will learn:

Solve absolute value inequalities in one variable. 
Graph the solution to an absolute value inequality on a number line. 
Solve and graph absolute value inequalities in real world contexts. 

# data[].attributes.body
In this lesson you will learn:

Solve absolute value inequalities in one variable. 
Graph the solution to an absolute value inequality on a number line. 
Solve and graph absolute value inequalities in real world contexts. 

# data[].attributes.body
l p + 2 l + 4 < 10

-6 < p + 2 < 6

-2   -2  -2

-8 < p < 4

# data[].attributes.body
-6< p+2 < 6
-2     -2     -2
-8  < p < 4

# data[].attributes.body
-6<p+2<6

-2   -2  -2

-8<p<4

# data[].attributes.body
|p + 2| < 6
-6 < |p + 2| < 6
-2          -2    -2
-8 < p < 4

# data[].attributes.body
-6<p+2<6
(subtract 2 from all sides)
-8<p<4
Answer: -8<p<4

# data[].attributes.body
[p+2]+4-4<10-4
-6<p+2<6

# data[].attributes.body
-6<p+2<6
-2   -2  -2
-8<p<4

# data[].attributes.body
-6<p+2<6 -2 -2 -2 -8<p<4

# data[].attributes.body
lp+2l+4<10
(-2 both sides)
-8<p<4

# data[].attributes.body
-6<p+2<6
-2      -2  -2
-8 <p <4

# data[].attributes.body
-6<p+2<6
-2    -2 -2
-8  <p  <4

# data[].attributes.body
-6<

# data[].attributes.body
-6<p+2<6
-2 from all sides

-8<p<4

# data[].attributes.body
-6< p+2 < 6
-2     -2   -2
-8 < p < 4

# data[].attributes.body
-6<P+2<6
-8<P<4

# data[].attributes.body
|p+2|+4<10
-6<p+2<6
-2      -2    -2
-8<p<4

# data[].attributes.body
-6<p+2<6
-2 from all sides
-8<p<4

# data[].attributes.body
-6<p+2<6
-2     -2  -2
-8<p<4

# data[].attributes.body
-6<p+2<6
(subtract 2 from all sides)
-8<p<4

# data[].attributes.body
|p + 2| + 4 < 10
Find the value of p.

# data[].attributes.body
|x-4|<3
-3<x-4<3
+4 all sides
1<x<7

# data[].attributes.body
|x-4|<3
-3<|x-4|<3
+4   +4 +4
1<x<7

# data[].attributes.body
lx-4l<3

-3<x-4<3

+4  +4  +4

1<x<7

# data[].attributes.body
-3<|x-4|<3
+4   +4  +4

1<x<7

# data[].attributes.body
lx-4l<3

-3<x-4<3

+4  +4  +4

1<x<7

# data[].attributes.body
-3<x-4<3
+4 +4  +4
1<x<7

# data[].attributes.body
lx-4l<3

-3<x-4<3

+4  +4  +4

1<x<7

# data[].attributes.body
-3<x-4<3
+4 +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
+4   +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
(add 4 to all sides)
1<x<7

# data[].attributes.body
-3<x-4<3 +4 +4 +4 1<x<7

# data[].attributes.body
-3<x-4<3
+4 +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
-3+4<x-4+2<3+4
1<x<7

# data[].attributes.body
-3<x-4<3
+4  +4  +4
1<x<7

# data[].attributes.body
-3<x-4<3
+4   +4 +4
1<x<7

# data[].attributes.body
-3<x<-4<3
1<x<7

# data[].attributes.body
-3<x-4<3
+4 +4  +4
1<x<7

# data[].attributes.body
-3<x-4<3
1>x>7 (add 4 to all sides)
Answer: 1<x<7

# data[].attributes.body
-3<x-4<3
+4 +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
+4  +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
+4   +4 +4
1<x<7

# data[].attributes.body
-3<x-4<3
(add 4 to all sides)
1<x<7

# data[].attributes.body
-3<x-4<3
+4   +4 +4
1<x<7

# data[].attributes.body
lx-4l<3
-3<x-4<3
add 4 all sides
Answer:1<x<7

# data[].attributes.body
|x-4|<3
-3<x-4<3
+4 all sides
1<x<7

# data[].attributes.body
|x-4|<3
Find the value of x.

# data[].attributes.body
|x+1|<3
-3<x+1<3
-1 from all sides
-4<x<2

# data[].attributes.body
-3<x+1<3
-1   -1    -1
-4<x<2

# data[].attributes.body
-3<x+1<3
-1    -1   -1
-4<x<2 answer

# data[].attributes.body
-3<x+ 1<3 -1 -1 -1 -4<x<2

# data[].attributes.body
lx+1l<3
-3<x+1<3
-1    -1  -1
-4<x<2

# data[].attributes.body
| x + 1 | = 3x
-3 < x -1 < 3

# data[].attributes.body
-3<x+1<3
-1   -1    -1
-4<x<2

# data[].attributes.body
-3<x+1<3
-4<x<2    subtract 1 from both sides
the answer is -4<x<2

# data[].attributes.body
|x+1|<3

-3<x+1<3

# data[].attributes.body
[x+1]<3
-3-1<x+1-1<3-1
-4<x<2

# data[].attributes.body
-3 < x +1 < 3
-1         -1     -1
-4<x<2

# data[].attributes.body
|x+1|<3
-3<x+1<3
-1    -1   -1
-4<x<2

# data[].attributes.body
-3<x+1<3
Subtract 1 from all sides
-4<x<2

# data[].attributes.body
-3<x+1<3
-1    -1  -1
-4<x<2

# data[].attributes.body
|x+1|<3
x+1-1<3-1          x+1-1>-3-1
x<2                     x>-4
Answer: -4<x<2

# data[].attributes.body
-3<x+1<3
-1    -1   -1
-4<x<2

# data[].attributes.body
-3<x+1<3
-1     -1   -1
-4<x<2

# data[].attributes.body
-3<x+1<3
-4<x<2 (subtract 1 from all sides)
Answer: -4<x<2

# data[].attributes.body
|x+1|<3
-3<x+1<3
-1 from all sides
-4<x<2

# data[].attributes.body
lx+1l<3
-3<x+1<3
-4<x<2 (subtract 1 from all sides)
Answer:-4<x<2

# data[].attributes.body
|x+1|<3
Find the value of x.

# data[].attributes.body
3x+2=3x (subtract 3x from both sides)
2=0 (no solution)

or

3x+2=-3x (subtract 2 from both sides)
3x=-3x-2 (add 3x to both sides)
6x=-2 (divide 6 from both sides)

-1/3=x

Answer: No Solution

# data[].attributes.body
This problem does not have a solution.

3|3x+2|=9x

3x+2=3x

-3x       -3x

2=0 No solution

3x+2=-3x

-3x       -3x

2\-6=-6x\-6

# data[].attributes.body
3x+2=3x        3x+2=-3x
-3        -3          -3        -3
2=0                  2=-6
x=no solution

# data[].attributes.body
3x+2=3x | 3x+2=-3x
-3x     -3x   +3x     +3x
2=0 2=-6

# data[].attributes.body
3x + 2 = 3x        |      3x + 2 = -3x
-3x      -3x             +3x      +3x
2=0                        2=6x

# data[].attributes.body
3|3x+2|=9x

3x+2=3x

-3x       -3x

2=0 No solution

3x+2=-3x

-3x       -3x

2\-6=-6x\-6

-

# data[].attributes.body
no solution

# data[].attributes.body
x3x+2=3x
-3x     -3x
2=0 or no solution

or

3x +2= -3x
+3x     +3x
6x=2
6x/6=2/2
x=-1/3

# data[].attributes.body
3x + 2= 3x          or           3x+2=-3x
-3x        -3x                        +3x       +3x
2=0                                            2=6
no solution

# data[].attributes.body
3x+2=3x
-3x       -3x
2=0 No solution

3x+2=-3x
-3x       -3x
2\-6=-6x\-6
-1\3=x

# data[].attributes.body
3x+2=3x        3x+2=-3x
-3        -3           -2        -2
2=0                 3x=-3x-2
6x=-2
6     6
x=-1/3
x=no solution

# data[].attributes.body
3|3x+2|=9x
3x+2=3x   or   3x+2=-3x
-3x  on both sides
2=0                   2=-6
no solution

# data[].attributes.body
3x + 2= 3x                     3x+2=-3x
-3x         -3x                    +3x       +3x
2=0 2=6

# data[].attributes.body
There is no solution

# data[].attributes.body
3x+2=3x (subtract 3x from both sides)
2=0 (no solution)

or

3x+2=-3x (subtract 2 from both sides)
3x=-3x-2 (add 3x to both sides)
6x=-2 (divide 6 from both sides)

-1/3=x

Answer: No Solution

# data[].attributes.body
3x + 2= 3x
-3x        -3x
2=0
no solution

3x + 2= -3x
-3x         -3x
-6\ 2 = -6x \ -6
-1/3 = x

# data[].attributes.body
3 I 3x+2 I = 9x
3x+2=3x  or   3x  + 2= -3x
-3x       -3x      -3x            -3x
2=0x                          2= -6x
divide -6x both sides
no solution           -1/3=x

# data[].attributes.body
3x + 2 = 3x   or   3x + 2 = -3x
-3x         -3x   or   -3x          -3x
2=0                or    2=-6x
(Divide by -6 on both sides)
No solution         -1/3 = x
There are no solutions