Download A. {5}

Skill Check
1) Write an algebraic expression to represent the verbal
expression 7 less than a number.
Answer:
n–7
2) Write an algebraic expression to represent the verbal
expression five more than the quotient of a number and 4.
Answer:
𝑥
4
+5
Unit 1-1:
Solving Equations
Example 1
Solve 𝟐𝒏 − 𝟓. 𝟒𝟖 = 𝟎. 𝟎𝟐
Answer:
The solution is 2.75.
Example 2
Solve
𝟓
− 𝒙
𝟖
Answer:
= 𝟐𝟎
The solution is –32.
Example 3
Solve 53 = 3(y – 2) – 2(3y – 1).
53 = 3(y – 2) – 2(3y – 1)
Original equation
53 = 3y – 6 – 6y + 2
Property.
Apply the Distributive
53 = –3y – 4
Simplify the right side.
57 = –3y
Add 4 to each side.
–19 = y
Answer:
Divide each side by –3.
The solution is –19.
Example 4
What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?
A. –6
B.
C.
D. 6
Skill Check
Add to Friday’s Notes
Example 5
What is the solution to
𝟑
𝟓
𝟏𝟓𝒅 + 𝟐𝟎 −
𝟏
𝟔
𝟏𝟖𝒅 − 𝟏𝟐 = 𝟑𝟖
Example 6
GEOMETRY The formula for the perimeter of a rectangle is
where P is the perimeter,
and w is the
width of the rectangle. What is this formula solved for w?
A.
B.
C.
D.
Assignment
Pg. 22-23
#9-17odd
#22, 23,
#37-41 odd
#45,
#49
Skill Check
Homework Assignment
Pg. 22-23
#9- z =53
#11: y = -8
#13- x = -6
#15- a = 3
#17- x = 4
#22 – 4n-6
#23 – 8𝑥 2
#37- y = -3
#39- x = -6
#41 – c = -3
#45#49-
𝐸
𝑚 = 2
𝑐
𝑦−𝑏𝑥−𝑐
𝑎=
𝑥2
Absolute Value
Example 5
Replace x with 4.
Multiply 2 and 4 first.
Subtract 8 from 6.
Add.
Answer:
4.7
Example 6
A. 18.3
B. 1.7
C. –1.7
D. –13.7
Example 7
Case 1 a = b
a = –b
Case 2
y+3 =8
y + 3 = –8
y+3–3 =8–3
y + 3 – 3 = –8 – 3
y = –11
y=5
Check
|y + 3| = 8
?
|5 + 3| = 8
|y + 3| = 8
|–11 + 3| = 8
?
|8| = 8
Answer:
?
8=8
The solutions are 5 and –11.
Thus, the solution set is –11, 5.
?
|–8| = 8
8 = 8
Example 8
What is the solution to |𝟐𝒙 + 𝟓| − 𝟓 = 𝟏𝟎?
A. {5}
B. {–10, 5}
C. {–5, 10}
D. {–5}
Skill Check
Example 9
Solve |6 – 4t| + 5 = 0.
|6 – 4t| + 5 = 0
|6 – 4t| = –5
This sentence is never true.
Answer:
The solution set is .
Original equation
Subtract 5 from each side.
Example 10
Money The U.S. Mint produces quarters that weigh about
5.67 grams each. After the quarters are produced, a machine
weighs them. If the quarter weighs 0.02 grams more or less
than the desired weight, the quarter is rejected. Write and
solve an equation to find the heaviest and lightest quarters
the machine will approve.
Skill Check
Assignment
Pg. 30-31
#17-35 odd