10-6 Class notes

To solve an inequality, simplifiy using the properties of equality (using the same operation on both sides of the inequality sign) until you get the variable by itself.

2x < 12, then divide both sides by 2 to get

x < 6

This gives us three things to graph:  A position (6), a dot (open because there's no equality line under the "less than" symbol), and a direction (to the left, the same way that the "less than" sign points).



When you are solving an inequality and you multiply or divide by a negative number, the negative sign causes the position and the direction to become opposites. Multiplying or dividing by the negative sign "flips" the sign of the number and it also "flips" the direction of the thick bar and arrow in the graph.

-2x < 12, then divide both sides by -2 to get

x > 6,  having changed the direction of the inequality from pointing left to pointing right.

10-5 Homework quiz

Wednesday 10-5 homework quiz

p37   11a, 11b, 12b

p38   1, 5

p44   a, b

Homework for Thursday 10-7

page 46; items a, b, c

9-30 Class notes and board shots

9-30 Class notes

Quiz on Monday, 10-3.  Some problems open notes; some problems from homework.

Homework for Monday, 10-3:  page 43; 9a, 9b and page 44; a, b, c.

Steps for graphing a one-variable inequality:

Simplify until you get the variable isolated on one side and a value isolated on the other side.
The value is the position on the number line.
Place an open dot at that position if there was no equal sign combined with the > or < symbol.
Place a closed dot if the inequality was > or < .
Shade a bar in the direction of the > (right) or < (left).

Position, type of dot, direction.

9-27 Solving multi-step equations

Answers to the homework from the weekend, page 37:

11a     -11/2
11b     10/8
11c     9/10
11d     5
12a     z = 0

In-class  problems and homework for 9-27 and 9-28:

page 37; items 12b, 12c
page 38; items 1, 2, 3, 4, 5, 6, 7, 8

9-23 Multi-step equations

There will be a homework quiz on Monday.  You may use your textbook and your notes to answer the questions.  The questions will be taken from the class notes, the homework, and the blog.

Answers for today's homework: 
10a.  x = -(11/15)
10b.  x = 8
10c.  no solution

Homework for Monday 9-26:  page 37; 11a, 11b, 11c, 11d, 12a

Hint for 12c:  Try to get a common denominator or try to clear the denominators (get rid of fractions)

After you simplify an equation, you may get to a statement that doesn't make sense.  If you have done the proper undoing, balancing, and operating equally on both sides, and you get a statement that is false,
such as 0 = 5, it means there is no solution to the equation.  There is nothing you can put in for x that will make the equation true.

If you simplify an equation and end up with a statement that is always true regardless of x, such as
5 = 5 or 2x = 2x, means the equation has infinite solutions.  No matter what you put in for x, the statement will be true.

Class notes 9-21 profit, other buttons, field trip

Homework for 9-22 is page 35, item 9, frequent visitor program