Chapter 2: Equations and Inequalities

 

1.      Solve:

a) -3x + 4 = -1     b) 5x - 1 = 4 + x     c) (3x - 2)2 = (x - 5)(9x + 4)

 

2.   Six hundred people attended the premiere of a motion picture.  Adult tickets

      cost $5, and children were admitted for $2.  If box office receipts totaled  

      $2400, how many children attended the premiere?  

 

3.   A bullet is fired horizontally at a target, and the sound of its impact is heard    

      1.5 seconds later.  If the speed of the bullet is 3300ft/sec and the speed of  

      sound is 1100ft/sec, how far away is the target?

 

4.   Solve the equations:

      a) x 2 = 169     b) 25x 2 = 9    c) 6x 2 - x = 2     d) 4x 2 + 81 = 36x

 

5.   A ball is thrown straight upward with an initial speed of 64ft/sec.  The number   

      of feet s above the ground after t seconds is given by the equation                            

      s = -16t 2 + 64t.

a)     When will the ball be 48 feet above the ground?

b)     When will it hit the ground?

 

6.      A closed cylindrical oil drum of height 4 feet is to be constructed so that the total surface area is 10π ft2.  Find the diameter of the drum.

 

7.   Find the solutions of the equations:

      a) x 2 - 6x + 13 = 0     b) x 2 + 8x + 17 = 0

 

8.   Solve the equations: (Hint: use substitution)

a) x 2/3 + x 1/3 - 6 = 0     b) x -2 - 2x -1 - 35 = 0

 

9.   Solve the inequalities & express the solutions in terms of intervals:

a) 3x - 2 > 14    b) 0 < 4 - x < 2     c) l2x + 5l < 4    d) l2x + 5l > 4