Life is all about Equations

Expressions are formed by variables and constants.

Variable don't have a fixed value and usually represented by letters (x, y, n, m, s)

Constants have fixed value and are represented by numbers(5, 9, 7, -5, 1/2)

Practical Usage of Expressions

1. 7 added to n = 7 + n
2. 7 subtracted from n = 7 - n
3. n multiplied by 7 = 7n
4. n divided by 7 = n / 7

Sara´s present age is x years.

What will her age be 10 years from now?   x + 10

What was her age 3 years back? x -3 

Sara´s cousin is 3 times her age : 3x

Sara´s sister is 2 years younger than her cousin : 3x – 2

Sara´s brother is 4 years older than her cousin: 3x + 4

Write the expression:

1. George is 3 years older than Ravi. Let´s say Ravi is x years old.

So George is years old.
2. My age is 2 years more than 5 times my cousin´s age. Let´s say my cousin´s  is n years old.

So my age  is  
3. Length of a park is 4 mts less than the breadth (b) of a park. What is the length (l) of the park?

 The length of the park is mts.
4. My age is 3 years less than 4 times my cousin´s age. Let´s say my cousin´s  is m years old.

So my age  is  
Equations: are expressions in which the value of

Left hand side(LHS) = Right hand side (RHS)

It cannot have > or <


Write if the expression is an equation with Yes (Y) or No (N)

1. 17 = x + 7 
2. t – 7 > 5    
3. 4 / 2 = 2   
4. 2m < 5     
5.  4x = 2     


2 types of Equations:

Variable Equations                                                             Numerical Equations

Equations with variables in them                                 Equations with only numbers and no variables

Example: 2n = 10                                                             Example: 8 - 3 = 5

x - 2 = 0                                                 20 - (10 -5) = 15
Complete the table and find the solution of x/3 = 4
x
8
9
10
11
12
13
14
15
16
x/3
8/3
9/3
10/3
11/3
12/3
13/3
14/3
15/3
16/3

x/3

      2
2  ___
      3

      

  3

      1
3  ___
      3
      2
3   ___
      3

     

    4

      1
4  ___
      3
      2
4 ___
      3

      

    5 

    

      1
5  ___
      3

So the solution of x/ 3 = 4 is 12 (x = 3* 4)

Complete the table and find the solution of m – 7 = 3

 

m  5 6 7 8 9 10 11 12 13
m-7     
 

So the solution of m – 7 = 3 is (m = 3 + 7).

Solving Equations

Adding, Subtracting, Multiplying or dividing on both sides
Example
 
 1.   x + 3 = 5
     x + 3 – 3  = 5 – 3      
     x + 0      =   2                       
         x        =   2                          
****************************
2.  x – 5 = 10
    x  –5 +5  = 10 + 5    
    x + 0    = 15                    
     x       = 15                       
****************************
3.   3n = 6              
      3n      6                                 
    ___ = ___   
     3         3
     n  = 2  
****************************
4.  p   
   ___   =  4             
   7
 
   7p         4* 7
____  =   
   7         
 
    p   =   28                      
****************************
5.  3s  = 10          
     __                        
      10                        
 10 * 3s   =  10 *  10
       ___    
        10
         3s    =  100
         3s   =   100
      _____     ____
          3          3
Adding, Subtracting, Multiplying or dividing on both sides
 
 
 1. Since we have a positive constant we are  going to add a negative constant to   cancel them out.
 
 
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2. Since we have a negative constant we are going to add a positive constant to    cancel them out
 
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3.  We divide both sides with a constant which  is multiplied to a variable.
    
 
 
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4.  This is a division problem. so we are going to multiply with the constant with which the variable is divided
 
 
 
 
 
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5.  This problem involves multiplication and division so we are going to divide and  multiply)
Transposing
 1.   x + 3  =  5
       x =  5 – 3
       x  =  2
 ***************************
2.   x – 5 =  10
       x   =     10 + 5
       x   =  15
 
***************************
3.   3n =  6
        n =   6
              ___   =   2
                3
         n   =  2
 
***************************
4 .    p  
      ___   =   4
        7
    p =   4* 7
    p  =   28
 
 
 
****************************
 5.    3s   
     ____  =  10
      10
 
      3s   =  10 * 10
 
     3s     =  100
      s       =   100
                   ____
                     3
 
 
 
 
when the constant changes the side , it changes its sign too.
 
 
 1. the positive constant when moved to the other side of the equal changes into a negative constant
 
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2. the negative constant when moved to the other side of the equal changes into a positive constant
 
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3. If it is multiplication , then the constant is divided with the constant of the variable.
    
 
 
****************************
4.  If it is division , then the constant is multiplied with the constant of the variable.
 
 
 
 
 
 
****************************
5.  This problem involves multiplication and division so we are going to divide and  multiply)
4(m + 3) = 8
4m + 12 = 8
4m = 8 -12
4m = -4
m = -1
 
 
4 = 5(p -2)
4 = 5p -10
4 + 10 = 5p
14 = 5p
14
__ = p
5
7m + 19 = 13         
          2
7m =  13 – 19
                  2
7m =   26 -19
               2
7m =  7
          2
m =   7                   
         2                    
         7       
         1       (It is assumed)
 =   7    *    1             =       7       =    1
     2           7                    14            2

 

-4 (2  + x) = 8
– – = 8
     –    = 8 +
     – = 
     – x = 
—
           x  =    – 
4 + 5 (p – 1) = 34
4  +   – = 34
4  + =  34  +
      = 34 + –
      =
     p = 
/
      p =
2b / 3
– 5 = 3
2b / 3
= 3 +
2b = 3 (3 + )
2b = ( )
2b =
b = 
/
 b =
                     
0 = 16 + 4(m – 6)
0 = 16 + –
0 = + m
= m
m = 
/
m =