solve the inequality analytically writing the solution set in interval notation. -10<4x+2 less then equal to 6.

Question

1. solve the inequality analytically writing the solution set in interval notation. -10<4x+2 less then equal to 6.

 

2. a salesperson has two jobs. Company A offers a weekly salary of $420 plus commission of 14% of sales. Company B offers a weekly salary of $840 plus commission of 7% of sales. what is the amount sales above which company A's offer is better of the two. 

Answer 1

 

 

1.

        -10< 4x+2 ≤6

   -10-2< 4x+2-2 ≤ 6-2

      -12 < 4x   ≤ 4 

     -12/4 < 4x/4  ≤ 4/4

     -3 < x   ≤ 1

or x  ∈ (-3, 1]

 

2.  let sales amount should be x

 

[420 + 14% of x] ≥ [840 + 7% of x]

  [420 + 0.14x]   ≥   [840 + 0.07 x]

    0.14x - 0.07x  ≥  840 - 420

                0.07x ≥  420 

                    x   ≥    420/0.07

                    x   ≥   6000

 

above $6000 sales amount company A's offer is better of the two.

Answer 2

-10 < 4x+2 

 

-12 < 4x   [subtracting 2 from both sides]

 

-3 < x       [dividing both sides by 4]

 

4x+2 ≤ 6

4x  ≤ 4    [subtracting 2 from both sides]

 

x ≤ 1   [dividing both sides by 4]

 

So the solution is -3 < x ≤ 1

 

You can draw a number line and boldface it from -3 to 1 with an open circle on -3 and a closed circle on 1.