Multiple Choice
Graph the solution of the inequality.
x ≤ 3
A. A solution is shown graphed on a number line. A number line has tick marks corresponding to numbers ranging between negative 9 and 9. A closed circle is shown on the number line at 3. The number line is shaded to the right of this closed circle.
B. A solution is shown graphed on a number line. A number line has tick marks corresponding to numbers ranging between negative 9 and 9. An open circle is shown on the number line at 3. The number line is shaded to the left of this open circle.
C. A solution is shown graphed on a number line. A number line has tick marks corresponding to numbers ranging between negative 9 and 9. A closed circle is shown on the number line at 3. The number line is shaded to the left of this closed circle.
D. A solution is shown graphed on a number line. A number line has tick marks corresponding to numbers ranging between negative 9 and 9. An open circle is shown on the number line at 3. The number line is shaded to the right of this open circle.
C
To graph the solution of the inequality x ≤ 3, follow these steps:
1. Draw a number line with tick marks that span from negative 9 to positive 9.
2. Place a closed circle at the number 3 on the number line. This indicates that the value of x can be equal to 3.
3. Shade the region to the left of the closed circle on the number line. This represents all the values of x that are less than or equal to 3.
Now, let's analyze the options provided:
A. This option states that the number line is shaded to the right of the closed circle at 3, which is incorrect.
B. This option states that an open circle is shown at 3, which is incorrect as the inequality includes 3.
C. This option states that a closed circle is shown at 3, and the number line is shaded to the left of this closed circle. This is the correct representation based on the given inequality x ≤ 3.
D. This option states that an open circle is shown at 3, and the number line is shaded to the right of this open circle, which is incorrect.
Therefore, the correct answer is option C: A solution is shown graphed on a number line. A number line has tick marks corresponding to numbers ranging between negative 9 and 9. A closed circle is shown on the number line at 3. The number line is shaded to the left of this closed circle.