Matching Number Lines with Absolute Values (2.14.1)

Question 1

• Absolute value is the distance a number is from 0 on the number line. It is always positive or equal to 0.

Answer 1

• Absolute value is the distance a number is from 0 on the number line. It is always positive or equal to 0.

Question 2

• An absolute value with a “less than” statement indicates that all the solution values are between the endpoints approaching 0.

Answer 2

• An absolute value with a “less than” statement indicates that all the solution values are between the endpoints approaching 0.

Question 3

• An absolute value with a “greater than” statement indicates that all the solution values are outside the endpoints moving away from 0.

Answer 3

• An absolute value with a “greater than” statement indicates that all the solution values are outside the endpoints moving away from 0.

Question 4

• The solution set for any inequality is shown by a line covering all possible values. The endpoints are shown with hollow dots or parentheses if the endpoints are not included in the solution set. The endpoints are shown with solid dots or square brackets if the endpoints are included in the solution.

Answer 4

• The solution set for any inequality is shown by a line covering all possible values. The endpoints are shown with hollow dots or parentheses if the endpoints are not included in the solution set. The endpoints are shown with solid dots or square brackets if the endpoints are included in the solution.

Question 5

Notice that the solution for this problem is shown by the bold line with the parentheses on –3 and +3. The bold line indicates that any value between –3 and +3 will satisfy the problem. The parentheses show that the endpoints are NOT included in the solution set. The variable can go to any value between –3 and +3 up to, but not including, those endpoints themselves.
In this problem, you see the bold lines indicating the solution set again. The square brackets on +4 and –4 indicate that they ARE included in the solution set for the problem. So this problem is solved by any value larger than and including +4 or smaller than and including –4.
Notice the solid dots here. They tell you that +4 and –4 are included in the solution set. The solid dots are an alternative to the square brackets. In this case, the hollow circles on +4 and –4 indicate that those values are NOT included in the solution set. They are an alternative to the parentheses.

Answer 5

Notice that the solution for this problem is shown by the bold line with the parentheses on –3 and +3. The bold line indicates that any value between –3 and +3 will satisfy the problem. The parentheses show that the endpoints are NOT included in the solution set. The variable can go to any value between –3 and +3 up to, but not including, those endpoints themselves.
In this problem, you see the bold lines indicating the solution set again. The square brackets on +4 and –4 indicate that they ARE included in the solution set for the problem. So this problem is solved by any value larger than and including +4 or smaller than and including –4.
Notice the solid dots here. They tell you that +4 and –4 are included in the solution set. The solid dots are an alternative to the square brackets. In this case, the hollow circles on +4 and –4 indicate that those values are NOT included in the solution set. They are an alternative to the parentheses.