1.06  Solving Inequalities

            Intermediate Algebra: One Step at a Time,  Pages 77 - 82:  #5, 10.

                                                                                                           Pages  88 - 90:  #6, 7, 8, 14.

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 1.06, with explanations, examples, exercises, and answers, click here!

p. 80.  # 5.  Solve for x. Give answers in interval notation:  

Solution:                            

Remove parentheses:                

Combine like terms:                        

Subtract 2x from each side:             

Subtract  17 from each side:        

Divide both sides by -5:                      

Reverse the Inequality:                           

                                                     

p. 81.  #10.  Solve for x. Give answers in interval notation:  

Solution:                  

Remove parentheses:       

Combine like terms:        

Add +3x to each side:    

Add +4 to each side:      

Divide both sides by −3:     

Reverse the Inequality:          

Interval notation:           

p. 89.  #6.  Solve for x. Give answers in interval notation:

                and  

Solution:  

“And” means “intersection”, so choose only the region that is common to both:

Interval notation:     [-2, 4)       

p. 89.  #7.  Solve for x. Give answers in interval notation:

                or  

Solution:  

“Or” means “union”, so choose ALL the regions that are shaded:

Interval notation:    [-2, ∞)       

p. 89.  #8.  Solve for x. Give answers in interval notation:

                and  

Solution:  

“And” means “intersection”, so choose only the regions that are common to both:

Interval notation:    [4, ∞)       

p. 90.  #14.  Solve for x. Give answers in interval notation:

                  and 

Solution:     and 

                               and     

“And” means “intersection”, so choose only the regions that are common to both.  This means the “overlapping region”, between -1 and 5.

Interval notation:    (-1, 5]