Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.5" was replaced by "(75/10)". 2 more similar replacement(s)

Rearrange:

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

                -x-(2*x+(69/10))-(x-(75/10))<0 

Step by step solution :

Step  1  :

            15
 Simplify   ——
            2 

Equation at the end of step  1  :

                69            15
  (-x -  (2x +  ——)) -  (x -  ——)  < 0 
                10            2 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          x     x • 2
     x =  —  =  —————
          1       2  

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 :

 2.2       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 • 2 - (15)     2x - 15
 ————————————  =  ———————
      2              2   

Equation at the end of step  2  :

                69      (2x - 15)
  (-x -  (2x +  ——)) -  —————————  < 0 
                10          2    

Step  3  :

            69
 Simplify   ——
            10

Equation at the end of step  3  :

                69      (2x - 15)
  (-x -  (2x +  ——)) -  —————————  < 0 
                10          2    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

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

           2x     2x • 10
     2x =  ——  =  ———————
           1        10   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 2x • 10 + 69     20x + 69
 ————————————  =  ————————
      10             10   

Equation at the end of step  4  :

         (20x + 69)     (2x - 15)
  (-x -  ——————————) -  —————————  < 0 
             10             2    

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

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

           -x     -x • 10
     -x =  ——  =  ———————
           1        10   

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 -x • 10 - ((20x+69))     -30x - 69
 ————————————————————  =  —————————
          10                 10    

Equation at the end of step  5  :

  (-30x - 69)    (2x - 15)
  ——————————— -  —————————  < 0 
      10             2    

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -30x - 69  =   -3 • (10x + 23) 

Calculating the Least Common Multiple :

 7.2    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       2 

      Least Common Multiple:
      10 

Calculating Multipliers :

 7.3    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 = 1

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 7.4      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.      -3 • (10x+23)
   ——————————————————  =   —————————————
         L.C.M                  10      

   R. Mult. • R. Num.      (2x-15) • 5
   ——————————————————  =   ———————————
         L.C.M                 10     

Adding fractions that have a common denominator :

 7.5       Adding up the two equivalent fractions

 -3 • (10x+23) - ((2x-15) • 5)     6 - 40x
 —————————————————————————————  =  ———————
              10                     10   

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   6 - 40x  =   -2 • (20x - 3) 

Equation at the end of step  8  :

  -2 • (20x - 3)
  ——————————————  < 0 
        10      

Step  9  :

 9.1    Multiply both sides by  10 

 9.2    Divide both sides by  -2 

Remember to flip the inequality sign:

 9.3    Divide both sides by  20  

      x-(3/20)  > 0

Solve Basic Inequality :

 9.4      Add  3/20  to both sides

             x > 3/20

Inequality Plot :

 9.5      Inequality plot for

         -4.000 X  + 0.600  >  0

  
 

One solution was found :