1.7 Linear and Absolute Value Inequalities

Question 1

a statement that two algebraic expressions are not equal in a particular way

Answer 1

inequality

Question 2

symbols for inequalities

Answer 2

Question 3

the set of all real numbers for which the inequality is true

Answer 3

solution set to an inequality

Question 4

4 different ways to express an inequality as a solution

Answer 4

1) graphically - number line with (), [ ]
2) inequality notation
3) interval notation
4) set-builder notation

Question 5

What is set-builder notation?

Answer 5

{variable | mathematical statement involving the variable. }

Question 6

What does “|” mean in mathematics?

Answer 6

“such that”

Question 7

intervals that use the infinity symbol

Answer 7

unbounded intervals

Question 8

the endpoint is not included in the interval and parenthesis used

Answer 8

open endpoint

Question 9

the endpoint is included in the interval - brackets used

Answer 9

closed endpoint

Question 10

a sentence containing two simple inequalities connected with the words “and” or “or”.

Answer 10

compound inequality

Question 11

an interval contains both of its endpoints

Answer 11

closed interval

Question 12

an inequality that does not involve infinity

Answer 12

bounded

Question 13

symbol for intersection

Answer 13

Question 14

symbol for union

Answer 14

Question 15

symbol for “is a member of”

Answer 15

Question 16

symbol for “is not a member of”

Answer 16

Question 17

In absolute value inequality problems, what must you remember?

Answer 17

1) Treat it just like an absolute value equation. Isolate the absolute value first. If you divide or multiply by a negative number in the isolation process, you must switch the direction of the inequality symbol.
2) Determine if the statement is an “and” or an “or”
3) Solve the inequalities.
4) Graph the solutions.
5) Make a decision about the final answer and write the answer in interval notation.

Question 18

When you multiply or divide by a negative number in an inequality statement, what must you remember?

Answer 18

switch the direction of the inequality symbol

Question 19

After isolating the absolute value, what type of problem do you have with a

Answer 19

“or” statement or union of two inequalities

Question 20

After isolating the absolute value, what type of problem do you have with a

Answer 20

“and” statement or the intersection of two inequalities

Question 21

what does “or” stand for with inequalities

Answer 21

union

Question 22

what does union mean?

Answer 22

putting answers together to make a combined statement that make an inequality true.

Question 23

what does intersection mean?

Answer 23

where the answers to inequalities overlap

Question 24

what does “and” stand for with inequalities

Answer 24

intersection

Question 25

when an endpoint is “included” as part of an answer in an interval, what symbol is used in interval notation?

Answer 25

brackets [ or ]

Question 26

when an endpoint is “not included” as part of an answer in an interval what symbol is used in interval notation?

Answer 26

parenthesis ( or )

Question 27

What symbol is used in interval notation for the infinities

Answer 27

parenthesis ( or )

Question 28

In algebra II, we used open circles on graphs. What have they been replaced with in College Algebra?

Answer 28

parenthesis ( or )

Question 29

In algebra II, we used closed circles on graph. What have they been replaced with in College Algebra?

Answer 29

brackets [ or ]

Question 30

If an inequality has an absolute value in the problem around the variable, how many inequalities must you set up?

Answer 30

2

Question 31

if an inequality does not have an absolute value in the problem around the variable, how many inequalities must you set up?

Answer 31

only 1

Question 32

When do you determine if the problem is an “and” or an “or” statement?

Answer 32

after isolation of the absolute value.