Solve, graph, and write the solution in interval notation. 1) |x| <= 3

kaeisky9u

kaeisky9u

Answered question

2022-08-02

Solve, graph, and write the solution in interval notation.
1. | x | 3
2. | x + 8 | < 6
3. | m 4 | 8 3
4. | a | > 7
5. | x 2 | 1 4
6. | x + 3 | > 8

Answer & Explanation

raffatoaq

raffatoaq

Beginner2022-08-03Added 22 answers

Step 1
1) | x | 3
x 3
x 3
x 3
x [ 3 , 3 ]
2) | x + 8 | < 6
x + 8 < 6
x < 6 8
x < 2
( x + 8 ) < 6
x 8 < 6
x < 6 + 8
x < 14
x > 14
x ( 14 , 2 )
3) | m 4 | 8 3
| m 4 | 3 + 8
| m 4 | 5
( m 4 ) 5
m 9
( m 4 ) 5
m + 4 5
m 1
m 1
m [ 1 , 9 ]
Step 2
4) | a | > 7
a > 7
a > 7
a < 7
a ( , 7 ) ( 7 , )
5) | x 2 | 1 4
| x 2 | 4 + 1
| x 2 | 5
x 2 5
x 7
( x 2 ) 5
x + 2 5
x 3
x 3
x ( , 3 ) [ 7 , )
6) | x + 3 | > 8
x + 3 > 8
x > 8 3
x > 5
( x + 3 ) > 8
x 3 > 8
x > 8 + 3
x < 11
x ( , 11 ) ( 5 , )

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