6.5 ANSWERS in-depth path

Answers exercise 1

Simplify

a) 5x + 4y - x - 7y 

= 5x + 4y - x - 7y 

= 4x - 3y 

 

b) -3v - - 6p + 3 + 4p 

= -3v + 6p + 3 + 4p 

= -3v + 6p + 3 + 4p 

= -3v + 10 p + 3 

 

c) -12ac + ac + 3a + 2c 

= -12ac + ac + 3a + 2c 

= -11ac + 3a + 2c 

Answer exercise 2

Look at the mathemagical video below and discover the math behind it. 

  1. We are going to call the number on the chosen card x. 
  2. I asked her to multiply the number on this card by 2 --> 2x
  3. Add 1 to her answer --> 2x + 1 
  4. Multiply her answer by 2 --> 2(2x + 1) = 4x + 2 
  5. Add the number on the chosen card --> 4x + 2 + x = 5x + 2 
  6. She had to multiply her answer by 2 --> 2(5x + 2) = 10x + 4 
  7. She had to add for the symbol on her card a different number: 

Spades: + 1 

Hearts: + 2 

Diamonds: + 3

Clubs: + 4

We call those symbols y --> 10x + 4 + y 

8. This is the formula behind the magical trick: 10x + 4 + y 

 

Now, try yourself