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### Problem 1: # Explanation: ## Step1: Identify the point and type The open point is at -3, and the line is shaded to the left. ## Step2: Determine the inequality Left - shaded open point means $ x < -3 $. # Answer: $ x < -3 $ ### Problem 2: # Explanation: ## Step1: Identify the point and type The closed point is at 5, and the line is shaded to the left. ## Step2: Determine the inequality Left - shaded closed point means $ x \leq 5 $. # Answer: $ x \leq 5 $ ### Problem 3: # Explanation: ## Step1: Identify the point and type The closed point is at 6, and the line is shaded to the right. ## Step2: Determine the inequality Right - shaded closed point means $ x \geq 6 $. # Answer: $ x \geq 6 $ ### Problem 4: # Explanation: ## Step1: Identify the point and type The open point is at -6, and the line is shaded to the right. ## Step2: Determine the inequality Right - shaded open point means $ x > -6 $. # Answer: $ x > -6 $ ### Problem 5: $ x\geq7 $ # Explanation: ## Step1: Identify the point and type We need to represent $ x\geq7 $. So, we place a closed point at 7 (since it's "greater than or equal to") and shade to the right. ## Step2: Draw on the number line On the number line from - 10 to 10, mark a closed circle at 7 and draw an arrow pointing to the right (towards 8, 9, 10, etc.). # Answer: (Closed circle at 7, arrow to the right) ### Problem 6: $ x < - 1$ # Explanation: ## Step1: Identify the point and type We need to represent $ x < -1 $. So, we place an open point at - 1 (since it's "less than", not "less than or equal to") and shade to the left. ## Step2: Draw on the number line On the number line from - 10 to 10, mark an open circle at - 1 and draw an arrow pointing to the left (towards - 2, - 3, - 10, etc.). # Answer: (Open circle at - 1, arrow to the left) ### Problem 7: $ x > - 8$ # Explanation: ## Step1: Identify the point and type We need to represent $ x > -8 $. So, we place an open point at - 8 (since it's "greater than", not "greater than or equal to") and shade to the right. ## Step2: Draw on the number line On the number line from - 10 to 10, mark an open circle at - 8 and draw an arrow pointing to the right (towards - 7, - 6, 0, 10, etc.). # Answer: (Open circle at - 8, arrow to the right) ### Problem 8: $ x\leq2$ # Explanation: ## Step1: Identify the point and type We need to represent $ x\leq2 $. So, we place a closed point at 2 (since it's "less than or equal to") and shade to the left. ## Step2: Draw on the number line On the number line from - 10 to 10, mark a closed circle at 2 and draw an arrow pointing to the left (towards 1, 0, - 10, etc.). # Answer: (Closed circle at 2, arrow to the left)

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Question

Explanation:

Problem 1:

Step1: Identify the point and type

Step2: Determine the inequality

Step1: Identify the point and type

Step2: Determine the inequality

Step1: Identify the point and type

Step2: Determine the inequality

Answer:

Problem 2: