Question

1. match each inequality to the correct graph.

1.
( overleftrightarrow{-7 -6 -5 -4 -3 -2 -1 0 1 \boldsymbol{\bigcirc} 3 4 5 6 7} )
a. ( x < 2 )
b. ( x < -2 )
2.
( overleftarrow{-7 -6 -5 -4 -3 -2 -1 0 1 \boldsymbol{oplus} 3 4 5 6 7} )
c. ( x > -2 )
d. ( x geq 2 )
3.
( overleftarrow{-7 -6 -5 -4 -3 \boldsymbol{oplus} -1 0 1 2 3 4 5 6 7} )
e. ( x < 5 )
f. ( x > 5 )
4.
( overleftrightarrow{-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 \boldsymbol{oplus} 6 7} )
5.
( overleftarrow{-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 \boldsymbol{oplus} 6 7} )
6.
( overleftrightarrow{-7 -6 -5 -4 -3 \boldsymbol{oplus} -1 0 1 2 3 4 5 6 7} )
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Explanation:

Step1: Analyze Graph 1

Graph 1 has a closed dot at 2 and the line goes to the right. A closed dot means the value is included, so this represents \( x \geq 2 \) (option d).

Step2: Analyze Graph 2

Graph 2 has an open dot at 2 and the line goes to the left. An open dot means the value is not included, so this represents \( x < 2 \) (option a).

Step3: Analyze Graph 3

Graph 3 has an open dot at -2 and the line goes to the left. So this represents \( x < -2 \) (option b).

Step4: Analyze Graph 4

Graph 4 has an open dot at 5 and the line goes to the right. So this represents \( x > 5 \) (option f).

Step5: Analyze Graph 5

Graph 5 has an open dot at 5 and the line goes to the left. So this represents \( x < 5 \) (option e).

Step6: Analyze Graph 6

Graph 6 has an open dot at -2 and the line goes to the right. So this represents \( x > -2 \) (option c).

Answer:

1. d. \( x \geq 2 \)
2. a. \( x < 2 \)
3. b. \( x < -2 \)
4. f. \( x > 5 \)
5. e. \( x < 5 \)
6. c. \( x > -2 \)