Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "13.5" was replaced by "(135/10)". 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 :

                     (18/10)*x-((135/10))≤0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            2 

Equation at the end of step  1  :

   18         27
  (—— • x) -  ——  ≤ 0 
   10         2 

Step  2  :

            9
 Simplify   —
            5

Equation at the end of step  2  :

   9         27
  (— • x) -  ——  ≤ 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.      9x • 2
   ——————————————————  =   ——————
         L.C.M               10  

   R. Mult. • R. Num.      27 • 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:

 9x • 2 - (27 • 5)     18x - 135
 —————————————————  =  —————————
        10                10    

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   18x - 135  =   9 • (2x - 15) 

Equation at the end of step  4  :

  9 • (2x - 15)
  —————————————  ≤ 0 
       10      

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Divide both sides by  9 

 5.3    Divide both sides by  2  

      x-(15/2)  ≤ 0

Solve Basic Inequality :

 5.4      Add  15/2  to both sides

             x ≤ 15/2

Inequality Plot :

 5.5      Inequality plot for

         1.800 X  - 13.500  ≤  0

  
 

One solution was found :