The document provides information on solving equations with variables on both sides, translating word problems into algebraic equations, and writing and interpreting decimals. It discusses that there are three possible results when solving equations with variables on both sides: 1) a single number solution, 2) no solution, or 3) infinite solutions. It also gives examples of translating word problems into algebraic equations and solving them. Finally, it addresses writing decimals in fractional form and interpreting decimals in various contexts.

2. News & Notes

3. 1. Perimeter of a Square: 2. Area of a Square:
P = 4S
The area of a square is actually the
same as the area of a rectangle: LxW
However, since the lengths of the sides are
the same, you are multiplying a number by
itself. So, the formula for the area of a square
is:
A = S2
Formulas

4. 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
a. Most of the equations we solve are conditional equations

5. 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
a) Known as Contradiction Equations
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.

6. 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
These are called identity equations. 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.
2. When solving these types of problems, write Infinite
Solutions on your paper.

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

8. Translating

9. Translating

10. A certain number, which first has 15 subtracted from it, then
has the difference multiplied by 7, will give a result of 28.
What’s the number? 7(x – 15) = 28 7x – 105 = 28
7x = 133; x = 19
Tell me the easier way to solve this
equation
x – 15 =
𝟐𝟖
𝟕
x – 15 = 4; x = 19
Be flexible, follow the path of least
resistance.
Translating

11. 1. Jane is nine years older than Marie. Jane is four
times as old as Marie. How old are each of the girls?
2. The sum of three consecutive odd numbers is 87.
What are the numbers?
Translating & Solving Word Problems
3. As the head pastry chef, you make $7.00/hr. So far you
have earned $42.00. Which of the following equations is
the algebraic model for this situation?
A. What does the variable represent?
B. What is the constant?

12. Let’s put all the algebra we’ve
learned so far to solve this:
2x + 1
2x + 1
xx
Perimeter =
50 ft.
Find the dimensions
of the rectangle?
(How long is the L & W)
The dimensions are: W = L =8 17

13. Writing & Interpreting Decimals