Download A. {5} - Pendleton County Schools

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 and Absolute
Value Equations
Example 1
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 2
What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?
A. –6
B.
C.
D. 6
Example 3
Surface area formula
Subtract πr 2 from each
side.
Simplify.
Example 3
Divide each side by
πr.
Simplify.
Example 4
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.
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}
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.
Assignment
Pg. 22-24
#24, 37, 40, 52, 58, 63
Pg. 30-31
#17, 22, 28, 33, 45