Transcript Slide 1

Component 2
The Language of Algebra
2
Language of Algebra
Stage 3
Stage 2
Stage 1
2
Language of Algebra
lease
Parenthesis (and other grouping symbols)
xcuse
Exponents
y
Multiply and divide from left to right
ear
unt
ally
Add and subtract from left to right
2
Language of Algebra
lease
xcuse
lease
y
Parenthesis
(and other grouping symbols)
ear
unt
ally
Grouping
Symbols
(and other grouping symbols)
Parenthesis
(12÷3) +1
Exponents
4+1
Multiply and divide from
left to right
5
Add and subtract from left
to right
2
Language of Algebra
lease
Parenthesis 3
5
means
2 – (8•2)
you4are
to use
5 as a factor
Exponents
2 – 16
34times
(and other grouping symbols)
xcuse
y
xcuse
Exponents
ear
unt
ally
16 – 16
Multiply and divide from
left to right 5•5•5
0
125
Add and subtract from
left to right
2
Language of Algebra
lease
Parenthesis
(and other grouping symbols)
xcuse
y
ear
Multiply and
y
divide from left
to right
ear
16 divided by
2 • 2 is 4
Exponents
8•2–7
Caution
4 –divided
7 = -3
16
!
by 8
is 2from left
Multiply and
divide
to right
2•2–7
unt
ally
Add and subtract from left
to right
2
Language of Algebra
16 ÷ 8 • 2 – 7
16 ÷ 16 – 7
1–7
-6
2
Language of Algebra
lease
Parenthesis
12 –
4•2+2
(and other grouping symbols)
xcuse
unt
ally
y
Add and subtract
from left to right
ear
unt
ally
Exponents
4•2
12 – 8 + 2
Multiply and divide from
4+2=6
left to right
Add and subtract from
left to right
2
Language of Algebra
60 ÷(32 + 1) – 2 • 2
lease
Parenthesis
(and other grouping symbols)
xcuse
Exponents
60÷10 = 6
y
ear
unt
ally
9+1 = 10
Multiply and divide from
left to right
2•2=4
6-4 = 2
Add and subtract from
left to right
2
Language of Algebra
lease
Parenthesis
(and other grouping symbols)
xcuse
Exponents
y
ear
unt
ally
Multiply and divide from
left to right
Add and subtract from
left to right
24
÷be
(xgiven
+ 2) an
You
will
UseSubstitute
PEMDAS to
find
the
expression
that
the
value
or
evaluate
number
value
for the
contains
variables
for
x
=
1
anvariable.
algebraic
and aexpression.
value to use for
the variable.
24 ÷ (1 + 2)
2
Language of Algebra
lease
Parenthesis
24 ÷ (x + 2)
for x = 1
(and other grouping symbols)
xcuse
Exponents
24 ÷ 3
y
ear
unt
ally
24 ÷ (1 + 2)
Multiply and divide from
left to right
Add and subtract from
left to right
8
2
Language of Algebra
2
x2(3
+
2)
50/x
(25) – –50/2
lease
Parenthesis
(and other grouping symbols)
xcuse
Exponents
for=x50
=2
2• 25
250
(3 ÷+ 22)=2 25
– 50/2
y
ear
Multiply and divide from
left to right
3+2= =25
5
50-25
52 = 25
unt
ally
Add and subtract from
left to right
PROPERTIES
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2
Language of Algebra
Now that you remember
how to simplify and
evaluate numerical and
algebraic expressions,
we are ready to use
these skills to solve
equations.
2
Language of Algebra
lease
Parenthesis
(and other grouping symbols)
xcuse
Exponents
y
Multiply and divide from
left to right
ear
unt
Distributive
Add and subtract from
5 left
Property
to right
ally
(x + 2)
2
Language of Algebra
AA= =5(5x)(x++2)
5(2)
5(x + 2) = 5(x) + 5(2)
or
5(x + 2) = 5x +10
x
(x + 2) 2
5
2
Language of Algebra
Solve for x.
x = 2(y+2)+2y
Copy this equation on
your paper and solve
for x.
Check your
Work
2
Language of Algebra
Did you find that
x = 4y + 4?
x = 2y + 4 +2y
In this example, how
would you solve for x
if y = 3?
Continue
2
Language of Algebra
Did you find that
x = 16?
Substitute
3 for y.
Substitute
16 for x.
16 = 2(3) + 4 +2(3)
Check your
Work
2
Language of Algebra
First,
More simplify
often, it both
is not.
sides
Two
Sometimes, the variable
guidelines
of the equation
will help you
you are solving for is
(ifwhen
needed)
you then,
meet use
an
isolated on one or the
inverse
equation
operations
such asto
other side of the = sign.
isolate
5x + 3(the
x +variable.
4) = 28.
2
Language of Algebra
5x + 3(x+4) = 28
Use what you have learned so far to
solve the equation for x.
Copy the equation onto your paper and
solve.
Check your thinking with the following.
Check your
Work
2
Language of Algebra
5x + 3(x+4) = 28
16 = 28
8x +
= 12
?
First, use
thefrom
distributive
Finally,
divide
both
sides
by the
Subtract
12
both
sides
to
property
like to
coefficient
of combine
the variable
isolate
theand
variable
term.
terms to
simplify
theand
leftsolve
side of
isolate
the
variable
the equation.
Check your
Work
PROPERTIES
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2
Language of Algebra
2 -2)
2 +16) = 10-3( m
¼ (12 m
PROPERTIES
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2
Language of Algebra
Component 1
This concludes Component 2.
1
Linear
Algebra
2
Rules of
Algebra
3
Using
Technology
4
Patterns of
Change