SECTION 3.1
ALGEBRA 1
Pass Skills 1.1d
OBJ: SOLVE EQUATIONS BY USING ADDITION & SUBTRACTION
SUBTRACTION PROPERTY OF EQUALITY
FOR ALL REAL #’S a,b,&c if a=b then a-c=b-c
SUBTRACTING EQUAL AMOUNTS FROM EACH SIDE OF THE EQUATION
RESULTS IN AN EQUIVALENT EQUATION.
“WHATEVER YOU DO TO ONE SIDE OF THE EQUATION YOU MUST DO TO THE
OTHER SIDE”
EXAMPLE 1 TRY THIS pg. 115
𝑎+5=4
−5 −5
𝑎=−1
1
1
+𝑛=11
2
2
1
1
−
−
2
2
𝑛=11
27.2=ℎ+45.6
−45.6 −45.6
−18.4=ℎ
ADDITION PROPERTY OF EQUALITY
FOR ALL REAL #’S a,b,c if a=b THEN a+c=b+c
ADDING EQUAL AMOUNTS TO EACH SIDE OF AN EQUATION RESULTS IN AN
EQUIVALENT EQUATION.
EXAMPLE 3 TRY THIS pg. 116
𝑎−5=7
+5 +5
𝑎=12
*GET THE VARIABLE BY ITSELF
−8=𝑛−3
+3 +3
−5=𝑛
ℎ−4.6=2.2
+4.6 +4.6
ℎ=6.8
SECTION 3.2
ALGEBRA 1
Pass Skills 1.1d
OBJ: SOLVE EQUATIONS BY USING MULTIPLICATION & DIVISION
THE DIVISION PROERTY OF EQUALITY
𝑎 𝑏
FOR ALL REAL #’S a,b,&c if a=b and c≠0 THEN =
𝑐 𝑐
DIVIDING EACH SIDE OF AN EQUATION BY EQUAL AMOUNTS RESLUTS
IN AN EQUIVALENT EQUATION.
“WHATEVER YOU DO TO ONE SIDE OF THE EQUATION YOU MUST DO
TO THE OTHER SIDE”
EXAMPLE 1 TRY THIS pg. 122
*GET THE VARIABLE BY ITSELF
EXAMPLE 2 TRY THIS pg. 123
6𝑥=72
−3=15𝑏
6 6
15 15
X=12
-1/5=b
EXAMPLE 3 TRY THIS pg.123
12𝑥 = 4.80
12
12
X= .40
THE MULTIPLICATION PROPERTY OF EQUALITY
FOR ALL REAL #’S a,b,&c if a=b THEN ac=bc
MULTIPLYING EACH SIDE OF AN EQUATION BY EQUAL AMOUNTS
RESULTS IN AN EQUIVALENT EQUATION.
*GET THE VARIABLE BY ITSELF
EXAMPLE 5 TRY THIS pg.124
𝑡
𝑑
=5
−3.2
𝑡
3
= −5.4
−3.2
𝑑 3
1
3 1
(
−3.2
3=
t=-16
(1.5)3 = ( )
1.5 1
d=-16.2
4.5=m
SECTION 3.2 CONT.
ALGEBRA 1
USING RECIPROCALS
USED WITH FRACTIONS
1
FLIP THE FRACTION
2
2
3
1
5
& ,
&
5
3
EXAMPLE 6 TRY THIS pg. 125
4m=
4𝑚
−3
2𝑑
8
5
−3
5 2𝑑
3 5
−4 3𝑥
8
2 5
2 2
5
=
1
1 4𝑚
4
(
1
=
8
=
3
−4
2
5
( )= ( )
−3 1
( )
4
d=
15
4
=3x
=
1
1 −4
( )
3
5
=
−3
−4
32
15
M=
1.5
𝑚 1.5
( ) = −5.4(3)
) =5(-3.2)
𝑚
3𝑥
1
=x
1
( )
3
SECTION 3.3
ALGEBRA 1
Pass Skills 1.1d
OBJ: WRITE EQUATIONS THAT REPRESENT REAL WORLD SITUATIONS
OBJ: SLOVE 2 STEP EQUATIONS
EXAMPLE 2 pg. 130 TRY THIS
15𝑦+31=61
−31 −61
15𝑦=30
15
15
−35=2𝑝+10
−10
−10
−45 =2𝑝
2 2
TRY & GET
THE VARIABLE
BY ITSELF.
Y=2
-22 ½ OR 22.5
EXAMPLE 3 pg. 131 TRY THIS
𝑚
𝑥
2
−4
-4.2= + 1.8
-1.8
-1.8
𝑚 2
2(-6) = ( )
2 1
− 3 = 10
-3 -3
−4
𝑥
1
−4
( )
-12=m
TALK ABOUT EXAMPLE 1 & 4 (WORD PROBLEMS)
= 13(-4)
x=-52
SECTION 3.4
ALGEBRA 1
Pass Skills 1.1d
OBJ: SOLVE MULTISTEP EQUATIONS
EXAMPLE 2 pg. 136 TRY THIS
5X-7 =4X+3
-4X
-4X
-3m +14 =5m +38
-3m
*GET VARIABLES ON ONE SIDE
14=8m+38
X-7 = 3
-38
+7 +7
-38
-24=8m
X=10
8
𝑋
X-2 = + 6
5
+2
𝑋
X= + 8
5
𝑋 5
8
-3=m
EXAMPLE 4 pg. 137 TRY THIS
+2
-3m
𝑋
6
5
5
1
1
5 (X-2)=( + )
5X-10=
𝑋
5
5
6
1
1
( )+
5X-10 = X +30
X= ( ) + 8(5)
+10
5X=X+40
5X= X+40
-X -X
-X –X
4X =40
4X = 40
4
4
5 1
4
X=10
X=10
+10
4
5
( )
1
SECTION 3.5
ALGEBRA 1
Pass Skills 1.1d
OBJ: USE THE DISTRIBUTIVE PROPERTY TO SOLVE EQUATIONS
EXAMPLE 2 pg. 143 TRY THIS
4t+7 –t =19
-7
-7
4t –t =12
3t =12
3 3
T=4
3M +2(4M-6) =10
3M +8M -12 =10
+12 +12
3M +8M =22
11M
22
11
11
M=2
5(P-2) =-15
5P-10 =-15
+10 +10
5P = -5
5
5
P=-1
EXAMPLE 3 pg. 143 TRY THIS
3(y-2) +4 =3y -2
3y-6 +4 =3y -2
7S +3 -2S =5S +6
-3
3y-2=3y-2
7S-2S =5S +3
THESE 2 EQUATIONS ARE =
5S = 5S +3
ALL REAL #’S
-5S -5S
0=3
THIS STATEMENT IS
FALSE NO SOLUTION
-3
SECTION 3.6
ALGEBRA 1
Pass Skills 1.1b
OBJ: SOLVE LITERAL EQUATIONS FOR A SPECIFIC VARIABLE
OBJ: USE FORMULAS TO SOLVE PROBLEMS.
LITERAL EQUATION
VARIABLES
AN EQUATION THAT INVOLVES 2 OR MORE
FORMULA A LITERAL EQUATION THAT STATES A RULE FOR A
RELATIONSHIP AMONG QUANTITIES.
TEMPERATURE FORMULA
5
C = (𝐹 − 32)
9
*PLUG THE # INTO THE
FORMULA FOR THE VARIABLE &
SOLVE
EXAMPLE 1 pg. 147 TRY THIS
a. 50°F
b. 212°F
5
5
9
C= (104 − 32)
9
5
5 18
9
9 1
C=10°
5
C= (212 − 32)
C= (50-32)
C= (18)
c. 104°F
( )
9
5
5 180
9
9
C= (180)
(
C=100°
1
)
5
5 72
9
9
C= (72)
C=40°
( )
1
MASS
𝑀
I=A-P
INTEREST
TOTAL
D=
PRINCIPAL
P=2l +2w
𝑉
DENSITY
VOLUME
PERIMETER
PARALLELOGRAM
A=1/2 h(B1+B2)
AREA OF
TRAPEZOID
TR
C=2𝜋𝑟
CIRCUMFERENCE
HEIGHT
LENGTH
BASES
PI
(3.14)
RADIUS
WIDTH