1. Simplifying Expressions
2 * x = 2x
A number times a variable, Smush together
5*y =
x * x = x2
A variable times a variable,
Use an exponent
z * z =
3x * 5 = 15x
Multiply the numbers, keep the variable
4y * 2 =
3x * x = 3x2
Multiply the variables, keep the number
7y * y =

2. Warm-Up
Ronisha and Kalyn are arguing whether the answer to 8(27) can be found by doing the following work.
Do you think this is correct? Explain.
Yes, this method can be used because 27 is still being multiplied by 8.
27 is just split into 20 and 7 first before it is multiplied by 8.

4. One-Step Equations and Inequalities
What is an equation?
My Definition
Two mathematical expressions that are set equal to one another.
Characteristics
Has an equal sign
Whatever you do to one side of the equal sign, you must do to the other side of the equal sign.
Examples
4 + x = 17
X – 5 = y
Non-examples
Y – 7 13
8x + 2y + 8
Equation

5. Inverse Operations
Inverse operations are operations that undo each other (opposites)
INVERSE OPERATIONS
Addition +
Subtraction -
Multiplication x
Division -
Square
Square Root
Recognizing Subtraction
Recognizing Multiplication
Recognizing Division
Recognizing Addition
Term with a negative sign in front
X – 5
-3 + x
Number & variable are side-by-side 5x xy
Number /variable are separated by fraction bar
𝑥 7
Positive number by itself
X + 3
3 + x

6. Do/Undo Method Solve for x + 7 = 22 DO UNDO Solve for x X = 15 Add 7
Subtract x + 7 = 22
x + 0 = 15

7. Think of this equation as a balance scale.
1) Solve r - 16 = 7
Think of this equation as a balance scale.
r - 16 7 =
Whatever you do to one side has to be done to the other to keep it balanced!

8. 1) Solve r - 16 = 7 To solve, you must get the variable by itself.
What number is on the same side as r? 16
To get r by itself, we must undo the “add 16”. What is the opposite of subraction?
Add 16

9. 1) Solve r - 16 = r - 16 = 7
r = 23
= 7
Draw “the river” to separate the equation into 2 sides
Subtract 16 from both sides
Simplify vertically
Check your answer by substituting your answer back into the problem

10. 2) Solve x + 2 = 3 Get the variable by itself. What is your first step?
Add 2 to both sides
Subtract 2 from both sides
Add 3 to both sides
Subtract 3 from both sides
Answer Now

11. 2) Solve x + 2 = 3
x = 1
1 + 2 = 3
Draw “the river” to separate the equation into 2 sides
Subtract 2 from both sides
Simplify vertically
Check your answer by substituting your answer back into the problem
On homework and tests, be sure to check your work!!
There is no reason why you should miss a problem!

12. 3) Solve 8 = m - 3
m = 5
m = 11
m = 24
m = 8/3
Answer Now

13. 3) Solve 8 = m - 3
11= m
8 =
Draw “the river” to separate the equation into 2 sides
Add 3 to both sides
Simplify vertically
Check your answer by substituting your answer back into the problem

16. Solution set of an inequality
Inequalities
Vocabulary
Write the term that best completes each statement.
A(n)________________ in one variable is the set of all points on a number line that makes the inequality true.
A(n) ___________________begins at a starting point and goes on forever in one direction.
Any mathematical sentence that has an inequality symbol is a(n)____________________________ .
The ____________________________is the set of all numbers that make the inequality true.
Word Bank
Inequality
Ray
Graph of an inequality
Solution set of an inequality

17. Key words

18. Examples of Graphs of Inequalities
X is equal to three
A number is at least a number is not more than 3
A number is greater than 3 a number is less than 3