Math 40
Chapter 2
Lecture Notes
Professor Miguel Ornelas
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M. Ornelas
Math 40 Lecture Notes
Section 2.1
Addition and Multiplication Properties of Equality
Addition Property of Equality
If A = B
then A + C = B + C
Multiplication Property of Equality
If A = B
then AC = BC
Addition Property of Equality
Solve each equation.
a. x + 10 = 21
1
8
=
3
3
c.
t+
e.
1
1
− +z =
5
2
Section 2.1 continued on next page. . .
b. −5 = x + 9
d. y −
7
5
=
6
8
f. −7.8 = 2.8 + x
2
Section 2.1
M. Ornelas
Math 40 Lecture Notes
Section 2.1 (continued)
Multiplication Property of Equality
Solve each equation.
a.
6x = 72
c.
a
= 15
3
d.
e.
2
x
=
7
−5
f. −3.4t = −20.4
b. −7y = −49
3
r = 27
4
Laura plays a basketball game in which she scores 19 points total with a combination of free throws, twopointers and three-pointers. If she made one free throw and three two-pointers, write an equation and find
the number of three pointers that she made.
Section 2.1 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 2.1 (continued)
Section 2.2
Solving Linear Equations
Solve each equation.
a.
2x + 5 = 9
b. −4x − 1 + 5x = 9x + 3 − 7x
c.
2(x − 3) = 5x − 9
d.
e.
−5(m − 3) + 2(3m + 1) = 15 − 8
f.
g.
2
1
2
1
x+ = x−
3
5
5
5
4
1
1
h. − − 2a = −
7
2 14
Section 2.2 continued on next page. . .
4
y y
1
− =
3 4
6
0.3x + 0.1 = 0.27x − 0.02
M. Ornelas
Math 40 Lecture Notes
Section 2.2 (continued)
Section 2.3
Formulas
Formula
I = P RT
Meaning
Interest = principal · rate · time
A = lw
Areas of rectangle = length · width
d = rt
Distance = rate · time
C = 2πr
Circumference of a circle = 2 ·π radius
V = lwh
Volume of a rectangular solid = length · width · height
Solving a Formula for a Specified Variable
Solve for the indicated variable.
a.
A = bh for h
c.
A=
e.
E = M C 2 for M
1
bh for b
2
g. h = vt + 16t2 for v
Section 2.3 continued on next page. . .
b.
3y − 2x = 9 for y
d. A = πr2 for r2
f. F =
9
C + 32 for C
5
h. A = P + P rt for P
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M. Ornelas
Math 40 Lecture Notes
Section 2.3 (continued)
Basic Percent Problems
a.
What is 20% of 78?
b.
What percent of 32 is 25?
If Maria paid in sales tax $3.24 on a $36 sweater, what percent of the total price was sales tax?
In 2011, Drew Brees of the New Orleans Saints completed 468 passes. This was 71.2% of his attempts. How
many attempts did he make?
Section 2.4
Problem Solving
1. The length of a rectangle is 5 inches more than twice the width. The perimeter is 34 inches. Find the
length and width.
Section 2.4 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 2.4 (continued)
2. Jaime is 3 years older than Michele. Four years ago the sum of their ages was 67. Find the age of each
person now.
3. Karina has $4.35 in nickels and quarters. If she has 15 more nickels than quarters, how many of each
coin does she have?
4. Raquel paid $68 for a pair of shoes during a 20%-off sale. What was the regular price?
Section 2.4 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 2.4 (continued)
Section 2.5
More Problem Solving
1. The second angle of an architect’s triangle is three times as large as the first. The third angle is 30◦
more than the first. Find the measure of each angle.
2. Adela is selling tickets to her play. Adult tickets cost $6.00 and children’s tickets cost $4.00. She sells
six more children’s tickets than adult tickets. The total amount of money she collects is $184. How
many adult tickets and how many children tickets did she sell?
3. Antwan has two savings accounts opened. The two accounts pays 10% and 12% in annual interest;
there is $500 more in the account that pays 12% than there is in the other. If the total interest for a
year is $214, how much money does he have in each account?
Section 2.5 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 2.5 (continued)
4. The houses on Elm street are consecutive odd numbers. Freddy Krueger and Michael Myers next-door
neighbors and the sum of their house numbers is 572. Find their house numbers.
5. In New York City, taxis charge $3.00 plus $0.40 per one-fifth mile for peak fares. How far can Lourdes
travel for $17.50 (assuming a peak fare)?
Section 2.6
Solving Inequalities
Solve and graph each inequality. Write the solution set using both set-builder and interval notation.
a. −2x + 7 ≥ 9
Section 2.6 continued on next page. . .
b.
9
3(x − 5) < 2(2x − 1)
M. Ornelas
Math 40 Lecture Notes
c.
4
− a − 2 > 10
5
d.
e.
8 − 6(x − 3) < −4x + 12
f.
Section 2.6 (continued)
7
4
11
7
y+ ≤
y−
6
3
6
6
3(m − 2) − 4 ≥ 7m + 14
Section 2.7
Compound Inequalities
Solve and graph each inequality. Write the solution set using both set-builder and interval notation.
a. x < −1 or x > 5
b.
Section 2.7 continued on next page. . .
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3x + 2 ≤ 11 and 2x + 2 ≥ 0
M. Ornelas
Math 40 Lecture Notes
c.
3x − 1 < 5 or 5x − 5 > 10
d.
e.
−7 ≤ 2x − 3 ≤ 7
f. −8 < 7x − 1 ≤ 13
Section 2.7 (continued)
3x + 9 < 7 or 2x − 7 > 11
The engine in a car gives off a lot of heat due to combustion in the cylinders. The water used to cool the
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engine keeps the temperature within the range 50 ≤ C + 32 ≤ 266. Solve this inequality and graph the
5
solution set.
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