Download Chapter Eleven Section One Introduction to Algebra Variable – a

10th Edition
Math – 10
Chapter Eleven Section One
Introduction to Algebra
Variable – a letter that can stand for various numbers.
Constant – a letter or number that doesn’t change or has one value.
Algebra Expression – a set of variables, constant, numbers, and operation signs
Evaluating the Expression – substituting values in for the variables.
Evaluate:
1.
a + b when a = 38 and b = 26 ( ) + ( ) = 38 + 26 = 64
2.
x – y when x = 57 and y = 29 ( ) – ( ) = 57 – 29 = 28
3.
4T
when T = 15
4 x ( ) = 4 x 15 = 60
When T = -6.8
4.
5.
6.
Area = L x W
௔
௕
ଵ଴௣
௤
4 x (-6.8) = -27.2
A = 24 x 8 = 192 ft2
when L = 24 ft and W = 8 ft
when a = -200 and b = 8
when p = 40 and q = 25
ିଶ଴଴
଼
= −25
ଵ଴௫ସ଴
ଶହ
=
ସ଴଴
ଶହ
= 16
Equivalent Expressions – two expressions that have the same value for all
allowable replacements.
For any Real Number:
a∙1=1 ∙ܽ=ܽ
Distributive Law of Multiplication:
a(b + c) = ab + ac a(b – c) = ab - ac
7.
Value of X
X =3
X = -6
X = 4.8
X
3
-6
4.8
1⋅ܺ
3
-6
4.8
1
Chapter 11
10th Edition
Math – 10
8.
Value of X
X=2
X = -6
X = 4.8
2X
4
-12
9.6
5X
10
-30
24
9.
Values of X and Y 5(X+Y)
X =6, Y = 7
5(6+7)
5(13)
65
X = -3, Y = 4
5(-3+4)
5(1)
5
X = -10, Y = 5
5(-10+5)
5(-5)
-25
5X+5Y
5(6)+5(7)
30 + 35
65
5(-3)+5(4)
-15 + 20
5
5(-10)+5(5)
-50+25
-25
10.
6X + 6Y
6(10)+6(5)
60+30
90
6(X+Y)
6(10+5)
6(15)
90
when X = 10 and Y = 5
11.
4(X+Y)
4(11+5)
4(16)
64
4X+4Y
(4x11)+(4x5)
44 + 20
64
when X = 11 and Y = 5
12.
7(X - Y)
7(9 – 2)
7(2)
14
7X – 7Y
(7x9) – (7x7)
63 – 49
14
when X = 9 and Y = 7
2
Chapter 11
10th Edition
Math – 10
13.
6X – 6Y
(6x10) – (6x5)
60 – 30
30
14.
2(X – Y)
2(11- 5)
2(6)
12
6(X – Y)
6(10 – 5)
6(5)
30
2X - 2Y
(2x11) – (2x5)
22-10
12
when X = 10 and Y = 5
when X = 11 and Y = 5
Terms – parts of expressions separated by ADDITION SIGNS
15.
5x – 4y + 3 (5x) +(-4y) + (3) 5x, -4y, 3
16.
-4y – 2x + 3z (-4y) + (-2x) + (3z) -4y, -2x, 3z
17.
3(x – 5) = 3x – 15
18.
5(x + 1) = 5x + 5
19.
ହ
ସ
ሺ‫ ݔ‬− ‫ ݕ‬+ 4ሻ =
ହ
ସ
‫ݔ‬−
ହ
ସ
‫ݕ‬+5
20.
-2(x – 3) = (-2)(x) – (-2)(3) = -2x + 6
21.
-5(x – 2y + 4z) = -5x + 10y – 20z
Factoring – reverse of multiplying
22.
6z – 12 = 6(z) – (6)2 = 6(z – 2)
23.
3x – 6y + 9 = 3(x) –(3)y + 3(3) = 3(x – y + 3)
24.
16a – 36b + 42 = 2(8a) – 2(18b) + 2(21) = 2(8a – 18b + 21)
25.
-12x + 32y – 16z = (-4)3x + (-4)(-8y) - (-4)(-4z) = -4(3x – 8y + 4z)
Collecting “LIKE” Terms
26.
6x – 3x = 3x
27.
7x – x = 6x
3
Chapter 11
10th Edition
Math – 10
28.
x – 9x = -8x
29.
x – 0.41x = 0.59x
30.
5x + 4y – 2x – y = (5x – 2x) + (4y – y) = 3x + 3y
31.
3x – 7x – 11 + 8y + 4 – 13y = (3x – 7x) + (8y – 13y) + (-11 + 4)
-4x – 5y – 7
32.
ଶ
ଷ
ଷ
ହ
− −
‫ݔ‬+‫ݕ‬+
(−
ଵ
ଵ଴
଻
ଵ଴
଺
ଵ଴
ଶ
‫ݔ‬−
‫ݔ‬+
ଽ
଻
ଵ଴
଻
ହ
ଵ଴
ଶ
ଶ
ଽ
ଷ
‫ )ݔ‬+ (y - ‫ݕ‬ሻ −
ଽ
ଶ
ଶ
ଽ
ଽ
ଷ
‫ )ݔ‬+( ‫ ݕ‬− ‫ )ݕ‬-
଻
ଶ
ଽ
ଷ
‫ݔ‬+ ‫ݕ‬-
ଷ
‫( = ݕ‬- ‫ ݔ‬+
Chapter Eleven Section Two Solving Equations: The Addition Principle
Solve = Just do the Opposite
1.
x + 2 = 11
-2
-2
X=9
2.
x+7=2
-7
-7
X = -5
3.
8.7 = n – 4.5
+4.5 +4.5
13.2 = n
4.
y + 17.4 = 10.9
-17.4 -17.4
y = -6.5
4
Chapter 11
10th Edition
Math – 10
Chapter Eleven Section Three
1.
Solving Equations: The Multiplication
Principle
6x = 90
଺௫
଺
ଽ଴
=
଺
X = 15
2.
4x = -7
ସ௫
ସ
= −
X=-
3.
଻
ସ
଻
ସ
-6x = 108
ି଺௫
ି଺
=
ଵ଴଼
ି଺
x = -18
4.
5.
-x = - 10
∙(-1) ∙(-1)
(-1)(-x) = (-1)(-10)
x = 10
ଶ
ହ
= − ‫ݕ‬
ଷ
ଶ
଺
଺
ହ
଺
ଷ
ହ
଺
ହ
( )(- ) = (- ‫()ݕ‬- )
−
ସ
ହ
=‫ݕ‬
5
Chapter 11
10th Edition
Math – 10
6.
1.12x = 8736
ଵ.ଵଶ௫
ଵ.ଵଶ
଼଻ଷ଺
=
ଵ.ଵଶ
X = 7800
7.
6.3 = - 2.1y
଺.ଷ
ିଶ.ଵ
=
ିଶ.ଵ௬
ିଶ.ଵ
-3 = y
8.
-14 =
ି௬
ଶ
ି௬
-14(-2) = ሺ
ଶ
ሻሺ−2ሻ
28 = y
6
Chapter 11