Solution - Linear inequalities

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "91.5" was replaced by "(915/10)".

Rearrange:

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

                     -3*q-((915/10))>0 

Step by step solution :

Step  1  :

            183
 Simplify   ———
             2 

Equation at the end of step  1  :

         183
  -3q -  ———  > 0 
          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 :

            -3q     -3q • 2
     -3q =  ———  =  ———————
             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:

 -3q • 2 - (183)     -6q - 183
 ———————————————  =  —————————
        2                2    

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -6q - 183  =   -3 • (2q + 61) 

Equation at the end of step  3  :

  -3 • (2q + 61)
  ——————————————  > 0 
        2       

Step  4  :

 4.1    Multiply both sides by  2 

 4.2    Divide both sides by  -3 

Remember to flip the inequality sign:

 4.3    Divide both sides by  2  

      q+(61/2)  < 0

Solve Basic Inequality :

 4.4      Subtract  61/2  from both sides

            q < -61/2

Inequality Plot :

 4.5      Inequality plot for

         -3.000 X  - 91.500  <  0

  
 

One solution was found :