Question

Which graph represents the solution set of the compound inequality?

−5<a−6<2



Responses

Number line ranging from negative ten to ten with arrows on both ends of the number line. A ray begins with an open point at negative five and continues to the left. A second ray begins with an open point at two and continues to the right.
Image with description Number line ranging from negative ten to ten with arrows on both ends of the number line. A ray begins with an open point at negative five and continues to the left. A second ray begins with an open point at two and continues to the right.

Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with an open point at one and ends with an open point at eight.
Image with description Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with an open point at one and ends with an open point at eight.

Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with an open point at negative five and ends with an open point at two.
Image with description Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with an open point at negative five and ends with an open point at two.

Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with a closed point at one and ends with a closed point at eight.
Image with description Number line ranging from negative ten to ten with arrows on both ends of the number line. A segment begins with a closed point at one and ends with a closed point at eight.

Answer 1

Add 6 to all parts: −5 < a − 6 < 2 implies −5+6 < a < 2+6, so 1 < a < 8.

Thus the graph is the segment from 1 to 8 with open endpoints — the second response.