Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Rearrange:

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

                (12/10)*x+(25/10)-(20)≤0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            2

Equation at the end of step  1  :

    12         5     
  ((—— • x) +  —) -  20  ≤ 0 
    10         2     

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

    6         5     
  ((— • x) +  —) -  20  ≤ 0 
    5         2     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       2 

      Least Common Multiple:
      10 

Calculating Multipliers :

 3.2    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 = 2

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 3.3      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.      6x • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      5 • 5
   ——————————————————  =   —————
         L.C.M              10  

Adding fractions that have a common denominator :

 3.4       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:

 6x • 2 + 5 • 5     12x + 25
 ——————————————  =  ————————
       10              10   

Equation at the end of step  3  :

  (12x + 25)    
  —————————— -  20  ≤ 0 
      10        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10  as the denominator :

          20     20 • 10
    20 =  ——  =  ———————
          1        10   

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 :

 4.2       Adding up the two equivalent fractions

 (12x+25) - (20 • 10)     12x - 175
 ————————————————————  =  —————————
          10                 10    

Equation at the end of step  4  :

  12x - 175
  —————————  ≤ 0 
     10    

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Divide both sides by  12  

      x-(175/12)  ≤ 0

Solve Basic Inequality :

 5.3      Add  175/12  to both sides

             x ≤ 175/12

Inequality Plot :

 5.4      Inequality plot for

         1.200 x  - 17.500  ≤  0

  
 

One solution was found :