Unit 2: Linear Equations

Simplifying Expressions

100

-3x -9 + 5x +17

2x + 8

200

3(x-2) + 2x

5x - 6

300

6.2 + 12x - 4.2 - 6.2x

5.8x + 2.2

400

-4/3(15x + 30) + 5

-20x -35

500

A rectangle has a length of 6 and a width of 5x - 3, write an expression to represent the perimeter of the rectangle. 

10x + 6

One & Two Step Equations

100

4x - 2 = 22

x = 6

200

x/3 -1 = 14

x = 45

300

5/6x -3 = 12

x = 18

400

17 - 1/9x = 10

x = 63

500

The perimeter of a rectangle is 36 inches.  Write and solve an equation to find the value of x. 

Length = 4x -6

Width = 12

x = 3

Multi-Step Equations

100

-2(3x -5) = 46

x = -6

200

1/5(30x - 10) = 10

_{x = 2}

300

-3/8(x - 24) + x = 19

x = 16

400

-0.5(22x + 10) = 17

x = -2

500

The area of a rectangle is 9 squared inches.  Set up and solve an equation to find the value of x.

Length= 3

Width = 1/9x - 2

45

Variables on Both Sides

100

5x -2 = 2x + 1

x = 1

200

8x -3 -1 = 13 x - 1 + 7

x = -2

300

3-5(x+4) = 8(2x -3)

x = 1/3

400

46 less than -8 times a number is the same as 8 less than -6 times the number.  

Write and equation and solve. 

The number = -19

500

The square and equilateral triangle have the same perimeter.  Write and solve an equation to find the value of x. 

Triangle side length: 2x + 8

Square side length: 2x + 5

x = 2

Special Cases (# of Solutions)

100

How many solutions are there for the following equation? 

5x -1 = 5x +3

No solutions

200

Solve the equation and name the number of solutions. 

10x + 2(x - 6) = 3(4x -4)

-12 = -12

All real numbers or Infinite Solutions

300

Solve and find the number of solutions:

8 + 4x = 2x + 8 + 3x

x = 0

One Solution

400

Solve the equation and name the number of solutions: 

2(9x - 6) = 6(3x - 2) + 2

-12 = -10

No Solution

500

Solve and then name the number of solutions: 

-1/5(30x - 10) = 2x - 1

x = 3/8

One Solution