Solving equations

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Good morning!

Schedule: 

• Learning goals 
• Solving equations
• Equations with a repeated variable

Learning goals 

At the end of this lesson I can:

• Solve 2-step equations

Why not trial and error?

Starter

Solve the following equations for x: 

a.  3(x - 4) = 39

b.                          

               

​2​​x−2​​=5

Starter

Solve the following equations for x: 

a. x = 17

   b. x = 12  

                         

What to do

Open this LessonUp on your device. 

Work on the slides with the appropriate color: 

- Got all the questions right                       I really want a challenge!

- Got 1-2 questions right                             I think a bit more practice will help me!

- Got 0-1 question correct                          I think more practice will help me! I                                                                                         would like some more help. 

Solving equations by backtracking

Step 1: Identify the operations in order

Step 2: Identify the inverse operations

Step 3: Apply inverse operations in REVERSE order

Example

​2​​x−2​​=5

Solving equations by backtracking

Step 1: Identify the operations in order

Step 2: Identify the inverse operations

Step 3: Apply inverse operations in REVERSE order

Example

Step 1:                                           Step 2:                               

-first 2 is subtracted from x         

-then we divide by 2                          

Step 3: 

​2​​x−2​​=5

Solving equations by backtracking

Step 1: Identify the operations in order

Step 2: Identify the inverse operations

Step 3: Apply inverse operations in REVERSE order

Example

Step 1:                                                        Step 2:                               

-first 2 is subtracted from x             -2           +2

-then we divide by 2                            /2            ⋅2

Step 3: 

​2​​x−2​​=5

Solving equations

3(x - 4) = 39 

1. Expand or simplify any brackets.

Solving equations

3(x - 4) = 39 

(3⋅x) + (3⋅ -4) = 39 

1. Expand or simplify any brackets.

Solving equations (1)

3(x - 4) = 39 

(3⋅x) + (3⋅ -4) = 39 

3x + (-12) = 39 

3x -12 = 39

 

Are all variables (x) on the same side?

2. Collect like terms

Solving equations

3(x - 4) = 39 

(3⋅x) + (3⋅ -4) = 39 

3x + (-12) = 39 

3x - 12 = 39 

3x -12 + 12 = 39 + 12

⋅ 3x = 51

3x/3 = 51/3

x = 17

3. Do Inverse operations on all terms on the side of x to

Isolate x

Solving equations

3(x - 4) = 39 

(3⋅x) + (3⋅ -4) = 39 

3x + (-12) = 39 

3x - 12 = 39 

3x -12 + 12 = 39 + 12

3x = 51

3x/3 = 51/3

x = 17

Solving equations by backtracking

3(x - 4) = 39 

Step 1: Identify operations

Step 2: Identify inverse operations

Step 3: Apply inverse operations in reverse order

Solving equations by backtracking

3(x - 4) = 39 

3(x - 4) / 3 = 39 / 3

x - 4 = 13

x - 4 + 4 = 13 + 4

x = 17

Step 1: Identify operations

Step 2: Identify inverse operations

Step 3: Apply inverse operations in reverse order

Let's get to work! 

p. 210-211: 10F            1adgj, 2be, 3abc, 5def

p. 211-212: 10F             3abcd, 4ac, 5adgj, 6cf

p. 211-212: 10F             5adgj, 6cf, 7adgjmps, 8def

Finished? Try the next level or pick up circuit training worksheet

Equations with variables on both sides

Worksheet

Finish the worksheet. 

Done? Pick up an answersheet from my desk and mark your work

Done? Pick up the circuit training worksheet from my desk