Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     (2*x-3)/5+2-(x/2)≤0 

Step by step solution :

Step  1  :

            x
 Simplify   —
            2

Equation at the end of step  1  :

   (2x - 3)          x
  (———————— +  2) -  —  ≤ 0 
      5              2

Step  2  :

            2x - 3
 Simplify   ——————
              5   

Equation at the end of step  2  :

   (2x - 3)          x
  (———————— +  2) -  —  ≤ 0 
      5              2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         2     2 • 5
    2 =  —  =  —————
         1       5  

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:

 (2x-3) + 2 • 5     2x + 7
 ——————————————  =  ——————
       5              5   

Equation at the end of step  3  :

  (2x + 7)    x
  ———————— -  —  ≤ 0 
     5        2

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       2 

      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 = 2

   Right_M = L.C.M / R_Deno = 5

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+7) • 2
   ——————————————————  =   ——————————
         L.C.M                 10    

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

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (2x+7) • 2 - (x • 5)     14 - x
 ————————————————————  =  ——————
          10                10  

Equation at the end of step  4  :

  14 - x
  ——————  ≤ 0 
    10  

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      x-14  ≥ 0

Solve Basic Inequality :

 5.3      Add  14  to both sides

             x ≥ 14

Inequality Plot :

 5.4      Inequality plot for

         -0.100 x  + 1.400  ≤  0

  
 

One solution was found :