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 :

                     -3/10*x-7-(1/2)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

           3                1
  ((0 -  (—— • x)) -  7) -  —  < 0 
          10                2

Step  2  :

             3
 Simplify   ——
            10

Equation at the end of step  2  :

           3                1
  ((0 -  (—— • x)) -  7) -  —  < 0 
          10                2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

         7     7 • 10
    7 =  —  =  ——————
         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:

 -3x - (7 • 10)     -3x - 70
 ——————————————  =  ————————
       10              10   

Equation at the end of step  3  :

  (-3x - 70)    1
  —————————— -  —  < 0 
      10        2

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -3x - 70  =   -1 • (3x + 70) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       2 

      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 = 1

   Right_M = L.C.M / R_Deno = 5

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.      (-3x-70)
   ——————————————————  =   ————————
         L.C.M                10   

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

Adding fractions that have a common denominator :

 5.5       Adding up the two equivalent fractions

 (-3x-70) - (5)     -3x - 75
 ——————————————  =  ————————
       10              10   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -3x - 75  =   -3 • (x + 25) 

Equation at the end of step  6  :

  -3 • (x + 25)
  —————————————  < 0 
       10      

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Divide both sides by  -3 

Remember to flip the inequality sign:

Solve Basic Inequality :

 7.3      Subtract  25  from both sides

            x > -25

Inequality Plot :

 7.4      Inequality plot for

         -0.300 X  - 7.500  >  0

  
 

One solution was found :