1. Today
Khan Academy Notes & Practice
Review for Final Exam (Next Week)
Review for |Absolute Value| Test (Thursday)
Usernames & Passwords for STAR math
Class Work

2. Schedule for this week:
Monday; Review for Tests, Tuesday; Meet in Room D101
Wednesday; Focus on absolute value, opposites/reciprocals,
Thursday; Absolute Value Test, Friday; Begin Inequalities
For the past 7 days, you have been on Khan Academy for
2403 minutes or 40.05 hours.
Topics for this week (Due November 2nd):
 Absolute Value Equations
 Linear Equation Word Problems
 Solving Rational Equations

4. Final Exam Review:
Translate
a. 8 less than the square of a number. 풙ퟐ − ퟖ
b. The sum of 25 and 5 times a number ퟐퟓ + ퟓ퐲
c. Four times the difference of a
number and four is eight
ퟒ(풙 − ퟒ) = ퟖ
The quotient of 7 and twice a number.
ퟕ
ퟐ풏
d.
e. Write & Solve: A number is seven
more than one-half of itself.

5. Final Exam Review:
Order of Operations: Simplify
10 - 2 - 3 + 36 ÷ 4 • 9
-1 - 2 - 3 • 4 - 5 = -20 86
Simplify Expressions
-5(1 – 5x) + 5( -8x -2)
- 15(x +1)
2p (q + 11q - 7)
2pq + 22qp – 14p =

7. Addition Rule
1) When the signs are the same,
ADD and keep the sign.
(-2) + (-4) =
2) When the signs are different,
SUBTRACT and use the sign of the larger number.
(-2) + 4 =
2 + (-4) =
-6
2
-2

8. What’s the difference between 7 - 3 and 7 + (-3) ?
7 - 3 = 4 and 7 + (-3) = 4
The only difference is that 7 - 3 is a subtraction
problem and 7 + (-3) is an addition problem.
“SUBTRACTING IS THE SAME AS ADDING
THE OPPOSITE.”

9. Example #1: - 4 - (-7) = - 4 + (7) =
3
Diff. Signs --> Subtract and use larger sign.
Example #2: - 3 – 7 = - 3 + (-7) -10
Same Signs --> Add and keep the sign.
Which is equivalent to -12 – (-3)?
1. 12 + 3
2. -12 + 3
3. -12 - 3
4. 12 - 3

10. Integers
Examples: Use the number line if necessary.
-5 0 5
(-4) + 8 = 4 (-1) + (-3) = -4
5 + (-7) = -2
(-5) -(-3) + (-2) + (6) – (4) = -2

11. -1 + 3 = ?
1. -4
2. -2
3. 2
4. 4
-6 + (-3) = ?
1. -9
2. -3
3. 3
4. 9
7 – (-2) = ?
1. -9
2. -5
3. 5
4. 9

13. The sum of two additive inverses (or opposites) is
equal to zero.
Example: The additive inverse of 3 is -3
Proof: 3 + (-3) = 0
The product of two multiplicative inverses
(or reciprocals) is equal to one.
Ex. The multiplicative inverse of 3 is
ퟏ
ퟑ
Proof: 3 •
ퟏ
ퟑ
= 1

14. Warm-Up/Review for Final Exam
Add the opposite & reciprocal of
ퟐ
ퟓ
to the opposite
& reciprocal of -
ퟏ
ퟒ
The opposite of what number divided by
ퟐ
ퟑ
is the
opposite of eight?
The reciprocal of what number a퐝퐝퐞퐝 퐭퐨
ퟕ
ퟒ
is two?

16. Absolute Value Equations:
A. - 13 = - |x + 3|
1. In other words, the opposite of
13 = the opposite of |x + 3|
2. The opposite of the opposites must also be equal: 13 = |x + 3|
3. The absolute value is isolated and equal to a positive number.
The two equations can now be written:
4. Solving for the positive value of the variable, the 1st equation is:
|x + 3| = 13; Solving for the possibility that the variable inside the
absolute value is negative, the 2nd equation is: |x + 3| = -13
10 - 16
The two possible solutions are x = and x =

17. Solving Absolute Value Equations
Write Each Step Needed to Solve
B. 5|x + 3|- 3 = 7
1. Add 3 to both sides. (When solving or ‘unwinding’
equations, we use the reverse of the order of operations,
always undoing whatever is connected to the variable last)
5|x + 3| = 10
2. Divide both sides by 5: |x + 3| = 2
3. Solving for the positive is the same equation after isolating the
absolute value.
|x + 3| = 2 4. Write the 2nd equation. |x + 3| = - 2
5. Solve each equation separately x = -1; x = -5
6. Plug each value into original equation to confirm solution
5|-1 + 3|- 3 = 7 5|-5 + 3|- 3 = 7

18. Solving Absolute Value Equations