Which graph shows the solution of 9 – c < 2 or –3c > 15?
(1 point)
Responses
–10 to 10 number line
Image with alt text: –10 to 10 number line
–10 to 10 number lineA closed point is shown at negative 5. A line goes from negative 5 to the arrow at the left end of the line. Another closed point is shown at 7. A line goes from 7 to the arrow at the right end of the number line.
Image with alt text: –10 to 10 number line A closed point is shown at negative 5. A line goes from negative 5 to the arrow at the left end of the line. Another closed point is shown at 7. A line goes from 7 to the arrow at the right end of the number line.
–10 to 10 number lineAn open point is shown at negative 5. A line goes from negative 5 through negative 6, negative 7, negative 8, negative 9, and negative 10 to the arrow at the left end of the line. Another open point is shown at 7. A line goes from 7 through 8, 9, and 10 to the arrow at the right end of the number line.
Image with alt text: –10 to 10 number line An open point is shown at negative 5. A line goes from negative 5 through negative 6, negative 7, negative 8, negative 9, and negative 10 to the arrow at the left end of the line. Another open point is shown at 7. A line goes from 7 through 8, 9, and 10 to the arrow at the right end of the number line.
–10 to 10 number line
Image with alt text: –10 to 10 number line
To determine which graph represents the solution of the compound inequality "9 – c < 2 or –3c > 15," we must first solve each inequality separately.
For the first inequality:
9 – c < 2
Subtract 9 from both sides:
– c < 2 - 9
– c < –7
Multiply both sides by –1 and reverse the inequality (since multiplying or dividing by a negative number reverses the inequality):
c > 7
This means that c must be greater than 7.
For the second inequality:
–3c > 15
Divide both sides by –3 (and remember to reverse the inequality):
c < –5
This means that c must be less than –5.
The solution to the compound inequality is c > 7 OR c < –5. Graphically, this is represented by a number line with the interval going from negative infinity to –5 with an open circle (exclusive) and another interval from 7 with another open circle to positive infinity.
Among the descriptions provided, the correct graph is the third one:
–10 to 10 number line An open point is shown at negative 5. A line goes from negative 5 through negative 6, negative 7, negative 8, negative 9, and negative 10 to the arrow at the left end of the line. Another open point is shown at 7. A line goes from 7 through 8, 9, and 10 to the arrow at the right end of the number line.
This graph represents all values of c that are less than –5 as well as all values of c that are greater than 7, which is the solution set for the given compound inequality.