This document contains notes and examples from a math lesson that covered several topics: 1) Simplifying expressions using order of operations and solving equations. Examples included 10 – 2 -3 + 36 ÷ 4 • 9 and -1 - 2 - 3 • 4 - 5 = -20. 2) Translating phrases to algebraic expressions such as "8 less than the square of a number" becoming x^2 – 8. 3) Solving fractional equations using the same process regardless of appearance, with examples like 1/3 x + 5/7 = 1/2. 4) Writing and solving word problems that can be translated to equations, such as one about Jay, Kay, and

1. TODAY:

2. Warm-Up:
Order of Operations: Simplify
10 – 2 -3 + 36 ÷ 4 • 9
86
-1 - 2 - 3 • 4 - 5 = -20
Simplify the expression.
+ 5x2 + 2x - 1
Solve the equations.
-5(1 – 5x) + 5( -8x -2) = -4x -8x
.15x + .6 = .63 0.5(x – 12) = .4

3. Translate from English to Algebra.
a. 8 less than the square of a number. 푥2 − 8
b. The quotient of 7 and twice a number. 7
2푛
c. The sum of 25 and 5 times a number 25 + 5y
d. Four less than the product
of four and x is nine. 4푥 − 4 = 9

4. Fractional Equations: Different Looks, Same Process
1.
ퟏ
ퟐ
x +
ퟓ
ퟑ
=
ퟏ
ퟔ
Warm-Up:
2. 5(4x – 3) + 2 = 37
3
a – 8 = 2a + 5
12 3
3.
5
1
4. x  x   2x
1 x
6
2
2
3
5. (
품
ퟑ
) + (
ퟐ
ퟓ
) = (
ퟑ
ퟐ
) - g
-x = 17 --We are not solving for
–x, do not leave like this
Either: a) Divide both sides by (-3) or b) Multiply
both sides by -1 at the end of the problem.

5. Writing & Solving Equations:
Jay, Kay, and Elle worked on a project together. Jay worked twice
as many hours as Kay. Elle worked 10 more hours than Kay. They
worked a total of 100 hours. How many hours did each work?
2. Andy is 2 times younger than his sister and his father
is 25 years older than him. If the total of their ages is 53
years, what is Andy’s age and his father’s age?

6. New Equations:
Whatever number we plug into x, the equation will be
true; it is an identity equation. The solutions are infinite

7. 1. If variables cancel and constants are not
equal, there are no possible solutions.
2. When solving these types of problems, write
No Solution on your paper.
on your own
1. Most of the equations we solve are conditional equations

8. Class Work
Work independently or in pairs
For All Assignments:
You Must Show Each Step of your solution.
Example: x + 5 = - 7
x = -7 - 5
x = - 12
-12 + 5 = - 7