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EXAMPLES & SOLUTIONS
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A non-linear equation does not form a straight line. It can have rational or irrational numbers in the equations.

The symbol sign (=) states that it is an equation.
It can have rational or irrational numbers in its' equation.
It can have degrees of 2 or more.
It is never straight, but always curved in someway.
NON-LINEAR EQUATION
Explanation of equations that are non-linear

equation:  x    -  3 - 7  = 15, x = ?

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Solve:

Follow properties and PEMDAS:

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      x   -  3 - 7 = 15  --combine terms & substract
           x    - 10 = 15  --updated expression
  x    - 10 + 10 = 15 + 10  --add 10 to both sides
     
   x    +  0   = 25  --square each side

              x     =      25 
   
            
x   =   + 5

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2

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Fact:  It is always good to verify (check) your answer.

Check:

Follow properties and PEMDAS:

    x    -  3 - 7  = ?  --substitute 5 for x (answer)
           5   - 10  = 15 --exponent rule 
    (5 * 5) - 10 = 15  --multiply
           25 - 10  = 15  --subtract rule
                      15 = 15  --CORRECT 

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      x    -  3 - 7  = ?  --substitute -5 for x (answer)
           -5   - 10  = 15  --exponent rule 
(-5 * -5)  - 10 = 15  --multiply 
             25 - 10  = 15  --subtract rule
                        15 = 15  --CORRECT 

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Non-Linear Equations
Examples of equations that are non-linear with even exponent

expression:  11 + 2x   + 4x   = 35, x = ?

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Solve:

6          6       

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2

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11 + 2x   + 4x    =  35  --exponent rule
           11 +  6x    =  35 --add coefficient, keep base 
      11 - 11 + 6x   =  35 -11  --subtract -11 from both sides
              0 + 6x   =  24  
                     6x   =  24  --updated equation
                     6x   =  24  --divide 6 from both sides
                                                           
                      x    =  4
                      
 x  =  + 2

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expression:  11 + 2x   + 4x   = 35, x = ?

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Check:

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          11 + 2(2)   + 4(2)    =  35   --substitute 2 for x
11 + 2(2 * 2) + 4 (2 * 2)  =  35  --exponent rule
              11 + 2(4 )+ 4(4)  =  35  --multiple rule
                         11 + 8 + 16  = 35  --subtract 7 from both sides
                               35  =  35
 --CORRECT

expression:  11 + 2x   + 4x   = 35, x = ?

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2

Check:

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2

               11 + 2(-2)   + 4(-2)    =  35   --substitute -2 for x
11 + 2(-2 * -2) + 4 (-2 * -2)  =  35  --exponent rule
                       11 + 2(4 )+ 4(4)  =  35  --multiple rule
                                   11 + 8 + 16  = 35  --subtract 7 from both sides
                                       35  =  35
 --CORRECT

Non-Linear Equations
Examples of equations that are non-linear with odd exponents

Solve:

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equation:   n    - 18 = 27, n = ?

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n

3

27

=

3

          n    - 18   =  9
n    + 18 - 18   = 9 + 18  --subtract 2 
from both sides
           n    +  0  = 27  --updated equation
      

                
  n  = 3

 

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Check:

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expression:  n    + 2  =  -6, n =  3 

                    n    - 18  =  9
                     3   - 18  =  9  --substitute 2 for x
                    3    - 18  =  9 --subtract 2 from both sides
   ( 3 * 3 * 3)  - 18 = 9
                    
 
27 - 18  = 9  --CORRECT
 

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