Algebra 1AB Name: __________________________ Date: ___________________________

Class#: __________________________  

3.1-3.4 Guided Notes  An  ___________________  is  a  number  sentence  or  relationship  noted  with  a(n)____________  sign.  Equations  can  be  solved  where:  

- there  is  exactly  _____________________  solution  - there  is  _______________________  solution  - there  are  ___________________________  solutions.  

 An  ______________________  is  a  number  sentence  noted  with  either  a  ____________________________  sign.    Inequalities  can  be  solved  where:  

- there  are  ______________________  solutions  - there  is  ____________________  solution  - Or  it  is  _____________________  numbers  

 Number  Sentence   Statement  in  Words   Description  in  words   Picture  

x = 2        

x > 2        

x ≥ 2        

x < 2        

x ≤ 2        

 

Is   x > 3the  same  as   3> x ?  Why  or  why  not?        You try! Rewrite  the  following  statements  so  that  the  variable  is  on  the  left.  

1.  4 < x   2.  32> y  

3.  −7 ≤ y  

Solving  inequalities  is  very  similar  to  solving  an  equation.  But  the  answers  are  very  different.    

Old  (Equation)   New  (Inequality)  Solve:  15  =  2x  +  21              Graph  the  solution:  

 

Solve:  15  <  2x  +  21              Graph  the  solution:  

         

       Examples Solve and graph the following.

1. 5 − x > 9

2. 4 < −2(x − 3)

3. −2 < −x − 3

4

21

Important  Rule  to  Remember  

   _________________________________________________________________________________________________  

Putting it all together Translate and solve the following: Example Translate Solve

1. 15 is greater than the sum of twice a number and 33

2. 15 greater than twice a number is 33

3. 15 is less than the sum of twice a number and 33

4. 15 less than twice a number is 33

5. 2 more than twice a number is more than 6

6. 2 more than twice a number is at least 6

7. 8 less and a number is less than 7

8. 8 less and a number is at most 7

Extension Circle the following that are in the solution set of 19153 ≤−x ?

{0, -9 , 8, -3, 1.5, 216 , 12, 2

15, 9.7, 100}

When solving an equation or an inequality and the variables cancel out, your answer is either _______________________ or ____________________________.

If you get a ______________ statement (i.e. 6 ≥ 6 ) your answer is __________________________________. If you get a ______________ statement (i.e. 6 > 6 ) your answer is __________________________________.

Modeling Real Life Applications

1. A prom ticket at Smith High School is $120. Tom is going to save money for the ticket by walking his neighbor’s dog for $15 per week. If Tom already has saved $22, what is the minimum number of weeks Tom must walk the dog to earn enough to pay for the prom ticket?

1. Define your variable: x = __________________________________________________

2. Write your number sentence to model the situation: _____________________________

3. Solve and graph the solution.

4. Interpret the solution in words.

2. There are 461 students and 20 teachers taking buses on a trip to a museum. Each bus can seat a maximum of 52. What is the least number of buses needed for the trip?

1. Define your variable: x = __________________________________________________

2. Write your number sentence to model the situation: _____________________________

3. Solve and graph the solution.

4. Interpret the solution in words.

3. Amir had $19 to spend at the carnival for admission and rides. If he paid $5 for admission, and rides cost $3 each, what is the maximum number of rides he could go on?

1. Define your variable: x = __________________________________________________

2. Write your number sentence to model the situation: _____________________________

3. Solve and graph the solution.

4. Interpret the solution in words.