2. Show Me Pictures
Another Great Definition of Learning
*A Life Lesson for All of Us
“It's not that I'm so smart, it's just that I
stay with problems longer.”
- Albert Einstein
~ A great graph and praise to this student for reasons that have
nothing to do with algebra. ~ It’s all about not giving up; not
quitting when things get tough. Stay with it and work harder,
not less. Not giving up is the ONLY way to achieve whatever it
is that you’d like to achieve. In this case....

3. Due on or before October 5, 7:00 pm
The root word of LINEar is?

4. Test #2: Class Averages

5. Equations..
...truly are the foundation on which Algebra is built upon.
We cannot just “test it and move on.”
Equations
What’s the point of moving on if we can’t ultimately close
out a problem by solving the equation?
Even if we can turn this into this, y = (x + 1)2 – 2= 0
if we can’t solve for x and y, we’ll not be able
to solve the problem.
We are still learning new equation types,
(literal, identity, absolute value). While learning
& practicing the new equations, we’re going to
have additional practice on those types of
equations we have covered so far.
Focus your efforts on understanding the rules common to all
equations. (Inverse Operations, Positive variable, etc.)

6. 1. The width of a rectangle is 2 more than one-half the
length. The perimeter is 89 yards. Find the length & width.
P = 89
Warm Up
9 – 6x = 2x + 1

7. Review
1. x + 4 = 11 2 . x - 5 = 8 1. 2x + 4 = 18 2. 3x - 5 = 10
Multi-Step Equations
* The same rules to solving equations apply, there are
just more steps to the solution.
1. 10y - (4y + 8) = -20
2. −8z −(2+3z) = 5(z + 3)

9. Solving Equations with Variables on Both Sides
 When an equation has variables on both sides,
three different results are possible.
 Write & solve this equation: 2x + 2 = 4 + x
The equation results in a solution of a single number.
In this case, x = 2

10. A 2nd Possibility
• 3x - 9 = 3x + 10
• A linear equation has NO SOLUTION when the
solved equation has no variable and the equation is
false.
3x - 3x = no variable, -9 = 10

11. A 3rd Possibility
• When an equation has variables on both sides,
something else may occur. Solve the equation:
4(x – 5) = 4x - 20
4x -20 = 4x -20; Subtract 4x from the left side and -20 = -20
This is called “identity”. It means ALL REAL
NUMBERS make the sentence true.
A linear equation is an identity when the solved
equation has NO VARIABLE and the solution is TRUE!
In other words, no matter what number we substitute
for x, the equation will be true.

12. Therefore…
• When solving equations with variables on both
sides, 3 different things can happen.
1) solution is a single number (x = 4)
2) solution is NO SOLUTION (empty set)
3) solution is ALL REAL Numbers ( IDENTITY)

13. Class Notes:
Tips for Solving Literal & Other Equations:
Literal Equations:
1. If the variable you are solving for is inside the
parenthesis, you must distribute first. 9p = 3(k + 5) for k
We need to separate the ‘k’ from the 5 in this case.
Solve the equation.
2. If the variable you are solving for is outside the
parenthesis, simply perform the opposite operation.
9 = k(p + 5) for k
3. When clearing fractions, if the denominator being
multiplied has two or more terms, it must be distributed on
the other side.
5k( 2p + 4) = 9
ퟓ풌
ퟑ
=
ퟑ
ퟐ풑+ퟒ
for p

14. Class Notes:
Class Notes:
Tips for Solving Literal & Other Equations:
4. Always check to see if every term has something in
common. You can then factor the common part out.
3kp – 7km – 9k – 1 = -7p + 10 for k
first
3kp – 7km – 9k = -7p + 11 Then,
k(3p – 7m – 9) = -7p + 11 Then
What?
k= -7p + 11
(3p – 7m – 9)

15. Class Notes:
Tips for Solving Literal & Other Equations:
5. If an entire term can be factored out, replace it
inside the parenthesis with a ‘1’
2p + 8px = ? 2p(1 + 4x) check by distributing the 2p again.
6. When solving fractional equations, you may have to
clear fractions more than once.
4 – 2x =
ퟏ
ퟓ
ퟔ − ퟑ풙
ퟑ 20 – 10x = 5
ퟔ −ퟑ풙
ퟑ
Complete the first step. Now we distribute the....
Solve for x.

16. Class Notes:
Tips for Solving Literal & Other Equations:
7. Two equal fractions is called a proportion.
Proportions can be solved by cross multiplying.
푺+ퟒ
ퟑ
=
ퟑ푺
ퟑ
solve
The following is not a proportion.
How must this problem be solved? Finish It

17. Class Work

18. Post-Test: 4 Most Missed
34% V. 3, Q 9
The first stage of a rocket burns 28 seconds longer than the second stage. If
the total burning time for both stages is 182 seconds, how many seconds
does the first stage burn for?
A) 124 B) 77 C) 98 D) 90 E) 105
32% V. 1, Q 8
- 6 = x -
ퟒ
ퟓ
(3 – x) A) 1
ퟏ
ퟒ
B) -3 C)
ퟑ
ퟒ
D)
ퟐ
ퟓ
E) -2

19. Post-Test: 4 Most Missed
30% V. 2, Q 5
4(2x – 2) = -8(x – 4)
The Most Difficult Question was.....
A) 2
ퟏ
ퟐ
B) 2 C) -2 D)
ퟑ
ퟒ
E) No Solution
ퟓ
ퟐ
= .....
26% V. 3, Q10
The sum of three consecutive even numbers is 132.
What is the largest of the three numbers?
A) 33 B) 44 C) 42 D) 46 E) 43