Solving Algebraic Expressions

Addition Principle

100

5x + 3 = 23

x = 4

200

5x - x = 8x +17 - 5x

x = 17

300

11x - x + 33 = 12x + x

x = 11

400

51 = 7 - 6x +2x

x = -11

500

2(3x - 4) - 9x - 5 = 2x +12

x = -5

Multiplication Principle

100

x/11 = 0

x = 0

200

x / -9 = -13

x = 117

300

x/2 + 10 = 4

x = -12

400

x-8 / 11 = 40

x = 448

500

2a−5=(2/3)a−3

a = 4

Division Principle

100

2x = -24

x =-12

200

-12x = 300

x = -25

300

106 = 4x +10

x = 24

400

2x - 110 = 11x - 146

x = 4

500

 Carlotta spent $35 at the market.  This was seven dollars less than three times what she spent at the bookstore; how much did she spend there?

3x − 7 = 35

x=14

Vocabulary

100

                                                                       

What is an expression?

                                                       

    

                                                                       

A mathematical combination of numbers, variables, and operations.

                                                       

    

200

                                                                       

What is an equation?

                                                       

    

                                                                       

A mathematical sentence stating that two expressions are equal.

                                                       

    

300

                                                                       

What are equivalent equations?

                                                       

    

                                                                       

Two equations that have the same solution

                                                       

    

400

What are terms?

numbers and/or variables separated by addition or subtraction symbols

500

What are like terms?

Terms that share the same variable raised to the same power.  (if there is no variable it is x⁰)

Find the Mistake!

100

x+9 = 15

x = 24

9 was added to each side instead being subtracted

200

3x + 5x = 16 and 8x = 16 are equivalent equations.

No Mistake

300

-4x = 19 + 13

-4x = 32

x = 8

If you divide each side by -4, your answer will be -8.

400

3x = 7 + 2x

5x = 7

x = 7/5

If you subtract 2x from each side, you will have x on the left side of the equation.

500

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

5x - 40 - 2x = -4x + 2

7x - 40 = -4x + 2 

11x - 40 = 2

11x = 44

x = 4

1. Combining the like terms of 5x and -2x will give you 3x - not 7x.

2. If you add 40 to each side, you will have 42 on the right - not 44.