Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.8" was replaced by "(48/10)". 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 :

                     x+(23/10)-((48/10))≤0 

Step by step solution :

Step  1  :

            24
 Simplify   ——
            5 

Equation at the end of step  1  :

        23     24
  (x +  ——) -  ——  ≤ 0 
        10     5 

Step  2  :

            23
 Simplify   ——
            10

Equation at the end of step  2  :

        23     24
  (x +  ——) -  ——  ≤ 0 
        10     5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

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

          x     x • 10
     x =  —  =  ——————
          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 :

 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:

 x • 10 + 23     10x + 23
 ———————————  =  ————————
     10             10   

Equation at the end of step  3  :

  (10x + 23)    24
  —————————— -  ——  ≤ 0 
      10        5 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      (10x+23)
   ——————————————————  =   ————————
         L.C.M                10   

   R. Mult. • R. Num.      24 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (10x+23) - (24 • 2)     10x - 25
 ———————————————————  =  ————————
         10                 10   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   10x - 25  =   5 • (2x - 5) 

Equation at the end of step  5  :

  5 • (2x - 5)
  ————————————  ≤ 0 
       10     

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  5 

 6.3    Divide both sides by  2  

      x-(5/2)  ≤ 0

Solve Basic Inequality :

 6.4      Add  5/2  to both sides

             x ≤ 5/2

Inequality Plot :

 6.5      Inequality plot for

         X  - 2.500  ≤  0

  
 

One solution was found :