1THV §9.5 Solving equations-Balance Method

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

1THV §9.5 Solving equations-Balance Method

In this LessonUp 

you will learn a Method to Solve equations.

It is different from the Book.

The advantage is that you can use it for all coming years too!

You get instructions by a two Movies.

The video in the next slide we skip.

Let's SOLVE an EQUATION together now!

Open your Notebook and

Take a pen from your pencilcase.

EXAMPLE 1

COPY the following equation:

SOLVE:

5c + 3 = 13

What could this mean in PRACTICE:  

5c + 3 = 13        ?!

This:    We have a BALANCE (=weegschaal) with. ON ONE HAND:

5 BAGS, all filled with c MARBLES and 3 loose MARBLES and

ON THE OTHER HAND: 

13 loose MARBLES.

We want to know how many marbles all the bags contain.

In other words: what number is c?!

Let us SOLVE the following equation:

(you don't have to copy the following yet)

5c + 3 =  13

How can we find out what number c is?! 

Let's make the equation SIMPLER:

•   We take away 3 from the LEFT.
• And we take away 3 from the RIGHT too!

We continue SOLVING the following equation:

5c + 3 = 13

•  We take away 3 from the LEFT.
•   And we take away 3 from the RIGHT too! 
  
•      5c = 10       We want to know how many marbles c is. So we
•   DIVIDE by 5 on BOTH sides of the balance:
•         c = 2              and this is the SOLUTION!                  

Now COPY the following:

5c + 3 = 13        (This line you already have writen down. If not, then DO IT                                          NOW!)

5c = 10

c = 2

TASK 1:

COPY and SOLVE with the BALANCE METHOD

(as you just learnt!):

7h + 34 = 83

The SOLUTION follows here!

Correct your own work or COPY this solution (NOT THE TEXT on the RIGHT!) if you did not manage to do it. 

• 7h + 34 = 83                  Let's take away 34 marbles on BOTH sides:
  
• 7h = 49                            We divide by 7 on BOTH sides:
• h = 7                                  So in all 7 bags there are 7 marbles.                          

Example 2

First this    Question:

 What are the NEW THINGS in this equation? 

SOLVE:

5      v  -   3     v  =   7  -   9     

​2​​1​​

​2​​1​​

NEW:      NEGATIVE NUMBERS and MORE TERMS!

It's pleasant that there are LIKE TERMS on both sides!

SOLVE:

5      v  -   3     v  =   7  -   9     

​2​​1​​

​2​​1​​

EXAMPLE 2

Let's SOLVE the following equation:

• 5      v  -   3     v  =   7  -   9          take the LIKE TERMS together
• 2 v = - 2                                          divide by 2 on both sides
• v = -1                        

   

​2​​1​​

​2​​1​​

We make the equation SIMPLER by

first SUBTRACTING the LIKE TERMS on the SAME SIDE:

SOLVE:

• 5     v   -   3     v  =   7  -   9    
• 2 v = - 2                            Let's DIVIDE by 2 on BOTH SIDES:
• v = - 1                                 As you see we are not talking about marbles any more... Negative numbers can appear as outcome too. 

​2​​1​​

​2​​1​​

TASK 2:

Copy and Solve with the Balance Method:

6      a -   3     a    =      12 - 18

​2​​1​​

​2​​1​​

TASK 2:

SOLUTION:

•                 6      a -   3     a    =  12 - 18     Take LIKE TERMS together:
•                  3 a = -6                                      DIVIDE by 3 on BOTH SIDES 
•                  a = - 2                                         A NEGATIVE solution again    

​2​​1​​

​2​​1​​

HOMEWORK:

§9.5

exercises        + 34, not c and e    35, 36 and 37

                             

One more thing ... see next slide! 

HOMEWORK:

Solve 34 t/m 37

with the BALANCE METHOD, that you learnt in this lesson.

Only writing down the outcome is not good enough.