Download Lesson 12 powerpoint

Jag Nation Pride
When you enter this classroom, immediately do the
following:
1. Take your seat.
2. Turn off all electronic devices and place in
backpack.
3. Take out all necessary materials (planner, binder,
pencil) and place back pack on floor under desk.
4. Read the Smart Board and follow all directions
posted. Copy homework assignment into planner.
5. Use a white board to complete any bell work that is
assigned.
BELLWORK
Write in set notation and graph the following solutions:
A.
B.
C.
Lesson 12
Solving Equations
Homework: S.67 #’s 1-6, 9-14, 17
STUDENT OUTCOME
The student will….
Be introduced to the formal process of solving an equation
Be able to explain each step of the properties of equality
Be able to identify equations that have the same solution.
Exercise 1:
(page S.63)
A. Use the commutative property to write an equation that
has the same solution set as:
B.
Use the associative property to write an equation that
has the same solution set as:
C.
Does this reasoning apply to the distributive property
as well?
Exercise 2:
(S.64)
Consider the equation:
A. Verify that this has the solution set {-3,2}. Draw this solution set as a graph on
the number line. We will later learn how to show that these happen to be the
ONLY solutions to this equation.
B.
Let’s add four to both sides of the equation and consider the new equation .
Verify 2 and -3 are still solutions.
C.
Let’s now add x to both sides of the equation and consider the new equation.
Are -3 and 2 still solutions?
continued on next slide
Exercise 2:
continued
Consider the equation:
D. Let’s add - 5to both sides of the equation and consider the new equation .
Are 2 and -3 still solutions?
E. Let’s multiply both sides by ⅙ to get
F. Let’s go back to part (d) and add
the new equation
/6 =1. Are 2 and -3 still solutions?
to both sides of the equation and consid
Are 2 and -3 still solutions?
Exercise 3:
A. Solve for r: 3/2r = 1/4
B. Solve for s:
C. Solve for y: 4y - 3 = 5y -8
(S.65)
Exercise 4:
Consider the equation
point.
Group 1: Subtract 3x from both sides.
Group 2: Subtract 4 from both sides.
Group 3: Subtract 8x from both sides.
Group 4: Add 16 to both sides.
(S.65)
Solve for x using the given starting
Closing
Consider the equation . Solve for
starting point.
(page S.66)
using the given
A. Use the commutative property to create an equatio wit hthe same
solution set.
B.
Using the result from (a), use the associative property to create an
equation with the same solution set.
C.
Using the result from (b), use the distributive property to create an
equation with the same solution set.
Lesson Summary
If is a solution to an equation, it will also be a solution to the new equation formed
when the same number is added to (or subtracted from) each side of the original
equation or when the two sides of the original equation are multiplied by (or divided
by) the same non-zero number. These are referred to as the Properties of Equality.
If one is faced with the task of solving an equation, that is, finding the solution set of
the equation:
Use the commutative, associative, and distributive properties, AND use the
properties of equality (adding, subtracting, multiplying by non-zeros, dividing by
non-zeros) to keep rewriting the equation into one whose solution set you easily
recognize. (We believe that the solution set will not change under these
operations.)
EXIT TICKET
Determine which of the following equations have the same solution set by
recognizing properties, rather than solving.
a. 2x + 3 = 13 - 5x
b. 6 + 4x = -10x + 26
c. 6x + 9 = 13/5 - x
d. .6 + .4x = -x + 2.6
e. 3(2x + 3) = 13/5 - x
f. 4x = -10x + 20
g.
15(2x + 3) = 13 - 5x
h. 15(2x +3) + 97 = 110 - 5x