Download Absolute Value Equations and Inequalities

Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
Name ___________________ Date ____________ Period ________
Section 3.7: Absolute Value Equations and Inequalities
*If you are absent the day we complete this handout together in class it is your responsibility
to fill it in; please borrow from a friend to get the notes you missed!
Day #1:

Absolute Value – the distance the number is from 0 on the number line.
o Ex. -3 and 3 are both 3 units from 0 on the number line. See below:

When dealing with absolute value and equality (=) you get rid of the absolute
value signs and write two equations. One equation will be set equal to a
positive number and the other will be set equal to the negative of that number.
When you graph on a number line you would just plot points. NO SHADING!

Let’s see some examples!
1. |n| = 9
Equation #1
Equation #2
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
2. | 2x – 5 | = 9
Equation #1
Equation #2
3. | x – 8 | = -11
Equation #1
Equation #2
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
4. 10 = |2g – 4|
Equation #1
Equation #2
5. -12 = |3m + 6|
Equation #1
Equation #2
Homework Assignment: P. 211: #10, 11, 17, 18, 19, 20p
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
Day #2:

When the absolute value equality has more than just an expression inside an
absolute value sign on one side of the equation, you must first isolate the
absolute value term. Once this has been done you write your two equations,
solve and graph.

Let’s see some examples:
1.
2|d| = 10
Equation #1
2.
Equation #2
-2|j| + 1 = 5
Equation #1
Equation #2
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
3.
|k + 1| - 2 = 5
Equation #1
4.
Equation #2
|4r + 1| - 2 = 5
Equation #1
Equation #2
Homework: P. 211: #s 11-16 AND #s 21-31
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
Day #3:

When dealing with absolute value and inequalities the type of inequality
determines if you’ll be using and “and” or “or”.
o Less than:

< or ≤  AND
Make two equations. The first just has the absolute value signs removed. The
second has a negative number and flips the inequality sign. Write the word
AND between the two equations. Remember that when graphing an “AND” you
usually get a dumb bell, but watch out for special cases! It is best to make 3
number lines (first inequality, second inequality and final answer (overlap.))
o Greater Than:
1.
(Think: “Less ThAND”)
> or ≥  OR
(Think: “GreatOR”)

Make two equations. The first just has the absolute value signs removed. The
second has a negative number and flips the inequality sign. Write the word OR
between the two equations. Remember that when graphing an “OR” you usually
get arrows pointing in opposite directions, but watch out for special cases! It
is best to make 3 number lines (first inequality, second inequality and final
answer (include everything that can be included.))

Let’s look at a few examples!
|p| ≥ -3
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
2.
| 2x + 7 | < 11
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
3. | 3 + 4x | ≤ 15
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
4.
8 < | n – 1|
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
5. -2 ≤ | 2h – 2|
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
Homework: P. 211: #s 32-46
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
Day #4:

When the absolute value inequality has more than just an expression inside an absolute value
sign on one side of the equation, you must first isolate the absolute value term. Once this has
been done you write your two equations, solve and graph.

Let’s look at some examples!
1.
-3|q| < -7
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
2.
-5 + |h| ≥ -13
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
Algebra I Chapter 3 Section 7: Quarter 2 Handout #3
3.
23 ≤ 2|w + 1|
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
4. -5|x + 2| ≥ 10
Equation #1
Equation #2
Final answer as a Compound Inequality: _________________________ and Interval Notation: ______________.
Homework: P. 211: #s 49-60