Solving Linear Equations

Vocabulary

100

Two expressions that are equal

What is an equation?

200

The process of adding or subtracting terms that are LIKE each other.

What is combining like terms?

300

Multiplying a number by a group of numbers added/subtracted together is the same as doing each multiplication separately. This is a form of SIMPLIFYING.

What is distribution or the distributive property?

400

Either a single number or a variable, or numbers and variables multiplied together that are separated by an operator

What is a term?

500

A group of terms that are separated by an operation

What is an expression?

Distribute +/or Combine

100

Distribute the following:

5(x + 2)

What is 5x + 2?

200

Combine the following:

-y + 7 + y² + 2y² + 3y + 4

What is 2y + 11 + 3y²?

300

Combine the following:

x + 5 - 2x - 10 + 5

What is -x?

400

Distribute the following:

-(x + -2 + -y)

What is -x + 2 + y?

500

Distribute and combine the following:

10(w+10) + 4(w+1)

What is 14w + 104?

1-Step Equations

100

Solve the equation:

4x = 16

What is x = 4?

200

Solve the equation:

-9x = -81

What is x = 9?

300

Solve the equation:

x - 14 = -6

What is x = 8?

400

Solve the equation:

x/2 = 7

What is x = 14?

500

Solve the equation:

x + 2 = -10

What is x = -12?

2-Step Equations

100

Solve the equation:

4(g - 1) = 24

What is g = 7?

200

Solve the equation:

16 - 7m = 30

What is m = -2?

300

Solve the equation:

3 - 9x = -6 - 8x

What is x = 9?

400

Solve the equation:

4(a + 1) = 2

What is a = -1/2 or a = -0.5?

500

Solve the equation:

(x/5) + 7 = -3

What is x = -50?

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

What is 8 years old?

Equation: x + 3 = 11

200

Mr. Dombrowski bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How much was each t-shirt?

What is $12.99?

300

Ms. Parisot has 4 boxes of apples. Each box has the same number of apples. After Ms. Parisot eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

What is 28 apples in each box?

400

Container A and container B have leaks. Container A has 800 ml of water and leaks 6 ml per minute. Container B has 1000 ml and leaks 10 ml per minute. How many minutes will it take the two containers to have the same amount of water?

What is 50 minutes?

500

The perimeter of a regular pentagon and square are the same. Each length of the pentagon is 0.5x + 2 and each length of the square is x - 2. What is the perimeter of each shape?

What is 40 units for each perimeter?

Multi-Step Equations

100

Solve the equation:

4(2a + 3) = -3(a - 1) + 31

What is a = 2?

200

Solve the equation:

-20y + 15 = 2 - 16y + 11

What is y = 0.5 or y = 1/2?

300

Solve the equation:

-3x - 4(4x - 8) = 3(-8x - 1)

What is x = -7

400

Solve the equation: 

13x - 9x + 20 = 30 + 2

What is x = 3?

500

Solve the equation:

2(x - 5) = 5x + 23

What is x = -11?