1. Unit 1: Hands on Equations
Final Exam Review

2. Topics to Include Solving 2-step equations
Solving multi-step equations
Equations with Negatives
Distributive Property
Vocabulary and Math Sentences
Word Problems

3. Solving 2-step Equations
The goal of solving equations is to get the variable BY ITSELF
To do this, you will need to first ADD or SUBTRACT, and then MULTIPLY or DIVIDE
Example: x – 2 = 10
Add 2  x = 12
Divide by 4  x = 3

4. Solving 2-step Equations
You Try!
1. 2x + 3 = x – 1 = 8

5. Solving multi-step equations
Always start by COMBINING LIKE TERMS on either side of the EQUALS SIGN
Example: x – x + 5 = 2x –
Combine like terms  3x + 5 = 2x + 11
Subtract 5  x = 2x + 6
Subtract 2x  x = 6

6. Solving multi-step equations
You Try!
1. 2x + 4x – 5 = 4x + 12 – 3
2. 5x + 2 – 9 = 3x + x – 7 + 3

7. Equations with negatives
When solving equations, be careful with the NEGATIVES!
A negative in front of a positive, will be NEGATIVE
Example: -5(3x) = -15x
A negative in front of a negative, will be POSITIVE
Example: -2(-4x) = 6x or 4 – (-3) = 4+3 = 7
EXAMPLE: (2x) + 5 = -x – 10
Multiply -3  x + 5 = -x – 10
Add x  x + 5 = -10
Subtract 5  x = -15
Divide by -5  x = 3

8. Equations with negatives
You Try!
1. -2(5x) – 20 = 5x – (-10) 2. x – 4 + (-3x) = 3 – (-2) + x

9. Distributive property
Use the Distributive Property when there is a number being MULTIPLIED by a polynomial.
Make sure you multiply the number by ALL TERMS in the polynomial.
Then you can COMBINE LIKE TERMS and solve for x.
Example: (x – 5) + 2 = 12
Distribute  x – = 12
Combine like terms  x – 8 = 12
Add 8  x = 20
Divide by 2  x = 10

10. Distributive property
You Try!
1. 3(x + 2) – 4 = (3x – 1) = 5(x + 3) – 5

11. Vocabulary and math sentences
Mathematical operations can be expressed by several difference vocabulary words.
For example, INCREASED BY means ADDITION and PRODUCT means MULTIPLICATION
You are going to practice writing mathematical sentences as expressions and vice versa.

12. Vocabulary and math sentences
Example: A number subtracted by eleven
x – 11
Example: x + 4 = 12
Three times a number plus four is twelve

13. Vocabulary and math sentences
You Try!
Write each sentence as an expression
The sum of five and a number
The product of six and a variable
Seven subtracted by a number is nine
Four times a number minus one is seventy

14. Vocabulary and math sentences
You Try!
Write each expression as a sentence
5x – 2
x + 13 = 4
x – 8 = 2x + 1
3(x – 1) = 9

15. Word Problems
Being able to solve word problems in math is very important.
It is the closest you will come to REAL-WORLD APPLICATION
Example: If three is added to twice a number, the result is 17. What is the number?
3 + 2x = 17
2x – 14
x = 7

16. Word Problems
You Try!
Three times a number, increased by one is twenty-five. What is the number?
Four times a number, plus three is equal to twice the number, increased by nine. What is the number?

17. ALL DONE