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EXAMPLES & SOLUTIONS
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A one-variable linear equation is an equation that has only one solution.

The symbol sign (=) states that it is an equation.
The expression on one side equals the expression on the other side.
The highest power of an one-variable equation is '1'.
x    is often written as 'x'.
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ONE-VARIABLE EQUATION EXAMPLE
Explanation of one-variable equations

equation:  x - 3 - 7 = 10, x = ?

Follow properties and PEMDAS:

 x - 3 - 7 = 10  --combine & subtract like terms
      x - 10 = 10  --updated expression
x - 10 + 10 =   10 + 10  --add 10 to both sides

        x + 0 =  20
          
    x = 20

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

Follow properties and PEMDAS:

Check:

    x - 3 - 7 = 10  --substitute 20 for x
 20 - 3 - 7 = 10 --subtraction rule
          17 - 7 = 10  --subtraction rule
                 10 = 10   
--CORRECT 

One Variable Equation
Examples of an one variable equations

equation: 7 + 3x + 4x = 35

Solve:

 7       7

7 + 3x + 4x  = 35  --combine & add like terms
            7 + 7x = 35 
     7 - 7 + 7x = 35 - 7  --substract 7 from both sides
           0 + 7x = 28
                   7x = 28  --updated equation
                   7x = 28  --divide 7 from both sides
                 
                    x = 28  

                             
                      
x = 4

7

--divide rule

Check:

 7 + 3x + 4x  = 35  --combine & add like terms
             7 + 7x = 35  --substitute 4 for x
    7 + (7 * 4) = 35  --multiply rule
            7 + 28  = 35  --addition rule
                     35 = 35 
--CORRECT

One Variable Equation
Another example of an one variable equations

equation:   5(n + 3) - 1 = 39

Solve:

              5(n + 3) - 1  = 39  --distributive property
 (5 * n) + (5* 3) - 1 = 39  --multiplication rule
                 5n + 15 - 1 =  39  --subtraction rule
                       5n + 14 = 39  

              5n + 14 - 14 =  39 -14  --subtract 14 from both sides
                        5n + 0 = 25
                                5n = 25  --updated equation
                               5n = 25  

                                    
x = 5

 5        5

--divide 5 from both sides

Check:

               5(n + 3) - 1  = 39  --substitute 5 for n
                5(5 + 3) - 1 = 39 --distributive property
(5 * 5) + (5 * 3) - 1  = 39  --multiplication rule
                   25 + 15 - 1 = 39  --addition rule
                            40 - 1 = 39  --subtraction rule
                                     39 = 39 
--CORRECT
 

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