Intro to HS Math Final Exam Review Name: ______

UNIT 1: HANDS ON EQUATIONS

Part 1: Solving 2-Step Equations

The goal of solving equations is to get the variable ______

To do this, you will need to first ______or ______, and then ______or ______

Example: 4x – 2 = 10

Add 2  4x = 12

Divide by 4  x = 3

You Try!

1. 2x + 3 = 152. 9x – 1 = 8

Part 2: Solving Multi-Step Equations

Always start by ______on either side of the______

Example: 4x – x + 5 = 2x – 4 + 15

Combine like terms  3x + 5 = 2x + 11

Subtract 5  3x = 2x + 6

Subtract 2x  x = 6

You Try!

1. 2x + 4x – 5 = 4x + 12 – 32. 5x + 2 – 9 = 3x + x – 7 + 3

Part 3: Equations with Negatives

When solving equations, be careful with the ______!

A negative in front of a positive, will be ______

Example: -5(3x) = -15x

A negative in front of a negative, will be ______

Example: -2(-4x) = 6x or 4 – (-3) = 4+3 = 7

EXAMPLE: -3(2x) + 5 = -x – 10

Multiply -3  -6x + 5 = -x – 10

Add x  -5x + 5 = -10

Subtract 5  -5x = -15

Divide by -5  x = 3

You Try!

1. -2(5x) – 20 = 5x – (-10)2. x – 4 + (-3x) = 3 – (-2) + x

Part 4: Distributive Property

Use the Distributive Property when there is a number being ______by a polynomial.

Make sure you multiply the number by ______ in the polynomial.

Then you can ______and solve for x.

Example: 2(x – 5) + 2 = 12

Distribute  2x – 10 + 2 = 12

Combine like terms  2x – 8 = 12

Add 8  2x = 20

Divide by 2  x = 10

You Try!

1. 3(x + 2) – 4 = 92. 4(3x – 1) = 5(x + 3) – 5

Part 5: Vocabulary and Math Sentences

Mathematical operations can be expressed by several difference vocabulary words.

For example, ______means ______and ______means ______

You are going to practice writing mathematical sentences as expressions and vice versa.

Example: A number subtracted by eleven : x – 11

Example: 3x + 4 = 12 : Three times a number plus four is twelve

You Try!

Write each sentence as an expression

  1. The sum of five and a number2. The product of six and a variable
  1. Seven subtracted by a number is nine4. Four times a number minus one is 70

You Try!

Write each expression as a sentence

  1. 5x – 22. x + 13 = 4

3. x – 8 = 2x + 14. 3(x – 1) = 9

Part 6: Word Problems

Being able to solve word problems in math is very important.

It is the closest you will come to ______

Example: If three is added to twice a number, the result is 17. What is the number?

3 + 2x = 17

2x – 14

x = 7

You Try!

  1. Three times a number, increased by one is twenty-five. What is the number?
  1. Four times a number, plus three is equal to twice the number, increased by nine. What is the number?

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