Find the solution set of the inequality below, using any method.

Question

Find the solution set of the inequality below, using any method. Give your answer in interval notation. Show all necessary work.

 

7 - (4/5)x > (3/5)

Answer 1

7 - (4/5)x > (3/5)

35 - 4x > 3          [multiply both sides by +5 retains sense of inequality]

  -4x > -32          [subtract 35 from both sides retains sense of inequality]

   4x < 32           [multiply both sides by (-1) reverses sense of inequality]

    x < 8             [divide both sides by 4 retains sense of inequality]

 

Test case: x=5

   Is   7 - (4/5)(5) > (3/5)   ?

         7 - 4  >  3/5   ?

          3  >  3/5   ?yes

 

Test case: x=10

  Is  7 - (4/5)(10) > (3/5)   ?

      7 - 8  > 3/5   ?

        -1  >  3/5   ?no