Solve 22.5 + x = -47.37.

x = -69.87

Step-by-step explanation:

22.5 + x = -47.37

Subtract the 22.5 on both sides:

x = - 69.87

(225/10)+x=-(4737/100)  

One solution was found :

                  x = -6987/100 = -69.870

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "47.37" was replaced by "(4737/100)". 2 more similar replacement(s)

Rearrange:

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

               (225/10)+x-(-(4737/100))=0  

Step by step solution :

Step  1  :

           4737

Simplify   ————

           100  

Equation at the end of step  1  :

  225                4737

 (——— +  x) -  (0 -  ————)  = 0  

  10                 100  

Step  2  :

           45

Simplify   ——

           2  

Equation at the end of step  2  :

  45          -4737

 (—— +  x) -  —————  = 0  

  2            100  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a whole to a fraction

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

        x     x • 2

   x =  —  =  —————

        1       2  

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 fractions that have a common denominator :

3.2       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:

45 + x • 2     2x + 45

——————————  =  ———————

    2             2    

Equation at the end of step  3  :

 (2x + 45)    -4737

 ————————— -  —————  = 0  

     2         100  

Step  4  :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

     The left denominator is :       2  

     The right denominator is :       100  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2122

5022

Product of all  

Prime Factors  2100100

     Least Common Multiple:

     100  

Calculating Multipliers :

4.2    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 = 50

  Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

4.3      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.      (2x+45) • 50

  ——————————————————  =   ————————————

        L.C.M                 100      

  R. Mult. • R. Num.      -4737

  ——————————————————  =   —————

        L.C.M              100  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions

(2x+45) • 50 - (-4737)     100x + 6987

——————————————————————  =  ———————————

         100                   100    

Equation at the end of step  4  :

 100x + 6987

 ———————————  = 0  

     100    

Step  5  :

When a fraction equals zero :

5.1    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:

 100x+6987

 ————————— • 100 = 0 • 100

    100    

Now, on the left hand side, the  100  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  100x+6987  = 0

Solving a Single Variable Equation :

5.2      Solve  :    100x+6987 = 0  

Subtract  6987  from both sides of the equation :  

                     100x = -6987

Divide both sides of the equation by 100:

                    x = -6987/100 = -69.870

One solution was found :

                  x = -6987/100 = -69.870

828. all there is to it!

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