10.1 Notes
Solving Equations – The Addition Principal
Vocab:
Solution –
Equivalent Equations –
The addition principal –
Examples:
1.
3.
x  7  12
a  5  14
10.2 Notes
2.
4  x  2
4.
x
1
3

2
4
Solving Equations – The Multiplication Principal
Coefficient –
The Multiplication Principal –
Tell whether you would use the addition or the multiplication principle.
1. x + 3 = -15
2. 2 x  20
Examples:
1. 2 x  20
2.  4 x  24
3.  x  8
c
5. 4  7
1
2
 x
4
3
4.
Problems to try:
1. Is 7 a solution for x  5  20 ?
Solve.
2. m  18  13
1
2
3. 8  y  12
1
5
5. 6    x
6.   z  
8.  x  1
9.
r
 4
5
4.  8  t  24
1
4
7. 3 x  15
10.
2
4
h
5
15
Solving multi-step equations.
Examples:
1. 5 y  3  12
2. 5 x  4  41
3.  91  9 y  8
4.  10 y  3 y  39
5. 4 x  6  6 x
6. 9  0.3(5 x  2)
7. 10  3(2 x  1)  1
8. 5  4 x  7  4 x  2  x
10. 5  x  3  x  2
9. 17  t  t  68
Solve for the indicated letter.
1. d  55h
3. y  x  A
4. y  bx  c
for h
for x
for x
2. y  mx
for x
3. W  mt  b
for t
5. y  2 x  bx
for x
6. The formula for perimeter of a rectangle is P = 2L +2W. If the length, L, is 9m
and the width, W, is 5m, find the perimeter, P, of the rectangle.
There are several ways to solve percent problems.
To set problems like these up as a proportion use the following patterns:
Example 1: 25 is what percent of 50?
is
%

of 100
or
part
%

whole 100
Example 2: What is 40% of 2?
Example 3: 40 is 2% of what number?
Another way to set up proportion problems is to set it up as
Amount = Percent number x base
Example 1: Sam, Selena, Rachel, and Clement left a 15% tip for a meal that cost $58. How much was the tip?
Example 2: Selena left a 15% tip of $8.40 for a meal. What was the cost of the meal before the tip?
Example 3: Paul takes out a student loan out for $2400. After a year, Paul decided to pay off the interest,
which is 7% of $2400. How much will he pay?
Example 4: The population of Grovestown was 2250 last year. This year it is 2295. What is the percent of
increase?
For % of increase/decrease use…
amt of change %

original
100
10.6 Applications and Problem Solving
10.7 Solving Inequalities
Inequality –
Graphing Inequalities –
Solution –
Solution Set –
We write answers for inequalities using two different ways:
a) set-builder notation
b) interval notation.
Example: Determine whether each number is a solution of the given inequality.
a) 0
c) -1
b) 5
d) -5
Example: Graph on a number line:
e) 6½
x5
Example: Graph on a number line: x  2
Example: Graph on a number line:  5  x  3
Example: Solve and Graph: x  5  2
Solve and graph:
a) 2x  4  x  7
b) 10  8  p
x5
c)
5x  25
d) 3x  4  8  x
Solving inequalities is exactly the same as solving an equation except when ________________________
_____________________________________________________________________________________
Solve and graph:
e)
 2x  12
g)
 4x  
1
5
i) 2(3  4m)  9  45
f) 20  5x
h)
j)
33  13  7 y
2 x 4
 
3 5 15
10.8 Application and Problems using inequalities
Translate:
1. A number is greater than -3.
2. Maggie scored no less than 92 on her English exam.
2. The average time it took to finish the test was between 45 and 55 minutes.
3. The price of the car is at most $21,900.
4. The average credit card holder is at least $4000 in debt.
Example: Your quiz grades are 74, 86, 89, and 91. Determine what scores on the last quiz will allow you to get
an average quiz grade of at least an 85.
Example: The women’s volleyball team can spend at most $450 for its awards banquet at a local restaurant. If
the restaurant charges a $40 set up fee plus $16 per person, at most how many can attend?
Example: RJ’s Plumbing and Heating charges $25 plus $30 per hour for emergency service. Gary remembers
being billed over $100 for an emergency call? How long was RJ’s there?