Which of the following is the solution to the inequality below? -3/2(x-1/3)> -5x

A. x> -3/35
B. x>2/21
C. x< 2/21
D. x< -3/35

1/3

Step-by-step explanation:

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

                    3/2*(x-1/3)-(-5*x)>0  

Step by step solution :

STEP

1

:

           1

Simplify   —

           3

Equation at the end of step

1

:

  3         1      

 (— • (x -  —)) -  -5x  > 0  

  2         3      

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

         x     x • 3

    x =  —  =  —————

         1       3  

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 • 3 - (1)     3x - 1

———————————  =  ——————

     3            3    

Equation at the end of step

2

:

  3   (3x - 1)      

 (— • ————————) -  -5x  > 0  

  2      3          

STEP

3

:

           3

Simplify   —

           2

Equation at the end of step

3

:

  3   (3x - 1)      

 (— • ————————) -  -5x  > 0  

  2      3          

STEP

4

:

Equation at the end of step

4

:

 (3x - 1)    

 ———————— -  -5x  > 0  

    2        

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1   Subtracting a whole from a fraction

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

          -5x     -5x • 2

   -5x =  ———  =  ———————

           1         2    

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

(3x-1) - (-5x • 2)     13x - 1

——————————————————  =  ———————

        2                 2    

The equation at the end of step

5

:

 13x - 1

 ———————  > 0  

    2    

STEP

6

:

6.1    Multiply both sides by  2  

6.2    Divide both sides by  13  

     x-(1/13)  > 0

Solve Basic Inequality :

6.3      Add  1/13  to both sides

            x > 1/13

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y