Question

X/2 + 1 = 1/4x - 6 solve for x

Answer 1

x=-28......................

Answer 2

Answer: x = -28

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x/2+1-(1/4*x-6)=0

                    1

Simplify      —

                   4

   x                         1          

 (— +  1)    -        ((— • x) -  6)  = 0  

  2                        4        

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

           6             6 • 4

   6 =  —  =  —————

          1             4  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (6 • 4)                               x - 24

———————————  =  ——————

     4                                            4  

 

   x                    (x - 24)

 (— +  1) -  ————————  = 0  

  2                 4    

                 x

Simplify   —

                 2

   x                  (x - 24)

 (— +  1) -  ————————  = 0  

  2                 4    

Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          1            1 • 2

   1 =  —  =  —————

         1              2  

Adding up the two equivalent fractions

  x + 2              x + 2

—————  =  —————

   2                    2  

         (x + 2)            (x - 24)

 ——————— -  ————————  = 0  

    2                               4    

Find the Least Common Multiple

     The left denominator is :       2  

     The right denominator is :       4  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left, Right}  

2 1 2 2

Product of all  

Prime Factors  2 4 4

     Least Common Multiple:

     4

Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_ Deno  

  Left_ M = L.C.M / L_ Deno = 2

  Right_ M = L.C.M / R_Deno = 1

Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      (x+2) • 2

  ——————————————————  =   —————————

        L.C.M                 4    

  R. Mult. •  R. Num.                                   ( x-24)

  ——————————————————  =   ——————

                      L.C.M                                            4  

Adding up the two equivalent fractions

(x+2) • 2 - ((x-24))                                           x + 28

————————————————————  =  ——————

         4                                                                  4  

     x + 28

 ——————  = 0  

     4  

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  x+28

 ———— • 4 = 0 • 4

   4  

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  x+28  = 0

Solve  :  x+28 = 0  

Subtract  28  from both sides of the equation :  

                     x = -28

I hope it is helpful?