Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.86" was replaced by "(286/100)". 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 :

                p+(352/100)-(-(286/100))≤0 

Step by step solution :

Step  1  :

            143
 Simplify   ———
            50 

Equation at the end of step  1  :

        352           143
  (p +  ———) -  (0 -  ———)  ≤ 0 
        100           50 

Step  2  :

            88
 Simplify   ——
            25

Equation at the end of step  2  :

        88     -143
  (p +  ——) -  ————  ≤ 0 
        25      50 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  25  as the denominator :

          p     p • 25
     p =  —  =  ——————
          1       25  

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:

 p • 25 + 88     25p + 88
 ———————————  =  ————————
     25             25   

Equation at the end of step  3  :

  (25p + 88)    -143
  —————————— -  ————  ≤ 0 
      25         50 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       50 

      Least Common Multiple:
      50 

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 = 2

   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.      (25p+88) • 2
   ——————————————————  =   ————————————
         L.C.M                  50     

   R. Mult. • R. Num.      -143
   ——————————————————  =   ————
         L.C.M              50 

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (25p+88) • 2 - (-143)     50p + 319
 —————————————————————  =  —————————
          50                  50    

Equation at the end of step  4  :

  50p + 319
  —————————  ≤ 0 
     50    

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  50  

      p+(319/50)  ≤ 0

Solve Basic Inequality :

 5.3      Subtract  319/50  from both sides

            p ≤ -319/50

Inequality Plot :

 5.4      Inequality plot for

         p  + 6.380  ≤  0

  
 

One solution was found :