Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     -2/5*x-9-(9/10)<0 

Step by step solution :

Step  1  :

             9
 Simplify   ——
            10

Equation at the end of step  1  :

          2                 9
  ((0 -  (— • x)) -  9) -  ——  < 0 
          5                10

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

          2                 9
  ((0 -  (— • x)) -  9) -  ——  < 0 
          5                10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

         9     9 • 5
    9 =  —  =  —————
         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 - (9 • 5)     -2x - 45
 —————————————  =  ————————
       5              5    

Equation at the end of step  3  :

  (-2x - 45)     9
  —————————— -  ——  < 0 
      5         10

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -2x - 45  =   -1 • (2x + 45) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 5.3    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 :

 5.4      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-45) • 2
   ——————————————————  =   ————————————
         L.C.M                  10     

   R. Mult. • R. Num.       9
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 5.5       Adding up the two equivalent fractions

 (-2x-45) • 2 - (9)     -4x - 99
 ——————————————————  =  ————————
         10                10   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -4x - 99  =   -1 • (4x + 99) 

Equation at the end of step  6  :

  -4x - 99
  ————————  < 0 
     10   

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Multiply both sides by (-1)

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

      4x+99  > 0

 7.3    Divide both sides by  4  

      x+(99/4)  > 0

Solve Basic Inequality :

 7.4      Subtract  99/4  from both sides

            x > -99/4

Inequality Plot :

 7.5      Inequality plot for

         -0.400 x  - 9.900  <  0

  
 

One solution was found :