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Transcript
Five-Minute Check (over Lesson 1–4)
CCSS
Then/Now
New Vocabulary
Key Concept: Addition / Subtraction Property of Inequality
Example 1: Solve an Inequality Using Addition or Subtraction
Key Concept: Multiplication / Division Property of Inequality
Example 2: Solve an Inequality Using Multiplication or
Division
Example 3: Solve Multi-Step Inequalities
Example 4: Write and Solve an Inequality
Over Lesson 1–4
Evaluate the expression |4w + 3| if w = –2.
Evaluate the expression |2x + y| if x = 1.5 and y = 4.
Evaluate the expression 5|xy – w| if w = –2, x = 1.5,
and y = 4.
Solve the equation |b + 20| = 21.
Solve the equation –4|a + 5| = –8.
What is the solution to the equation
2|3x – 1| – 1 = –5?
Over Lesson 1–4
Evaluate the expression |4w + 3| if w = –2.
A. 5
B. 7
C. 11
D. 12
Over Lesson 1–4
Evaluate the expression |2x + y| if x = 1.5 and y = 4.
A. 5
B. 7
C. 10
D. 20
Over Lesson 1–4
Evaluate the expression 5|xy – w| if w = –2, x = 1.5,
and y = 4.
A. 5
B. 10
C. 20
D. 40
Over Lesson 1–4
Solve the equation |b + 20| = 21.
A. {–41, 1}
B. {–41, –1}
C. {–1, 1}
D. {1, 2}
Over Lesson 1–4
Solve the equation –4|a + 5| = –8.
A. {7, 3}
B. {2, 3}
C. {–7, –3}
D. {–2, 3}
Over Lesson 1–4
What is the solution to the equation
2|3x – 1| – 1 = –5?
A.
B.
C.
D.
Content Standards
A.CED.1 Create equations and inequalities in
one variable and use them to solve problems.
A.CED.3 Represent constraints by equations
or inequalities, and by systems of equations
and/or inequalities, and interpret solutions as
viable or nonviable options in a modeling
context.
Mathematical Practices
4 Model with mathematics.
You solved equations involving absolute
values.
• Solve one-step inequalities.
• Solve multi-step inequalities.
• set-builder notation
For example: {x | x  –7}
Solve an Inequality Using Addition or Subtraction
Solve 4y – 3 < 5y + 2. Graph the solution set on a
number line.
4y – 3 < 5y + 2
4y – 3 – 4y < 5y + 2 – 4y
–3 < y + 2
–3 – 2 < y + 2 – 2
–5 < y
y > –5
Original inequality
Subtract 4y from each
side.
Simplify.
Subtract 2 from each
side.
Simplify.
Rewrite with y first.
Solve an Inequality Using Addition or Subtraction
Answer: Any real number greater than –5 is a solution
of this inequality.
A circle means that this
point is not included in
the solution set.
Which graph represents the solution to
6x – 2 < 5x + 7?
A.
B.
C.
D.
Solve an Inequality Using Multiplication
or Division
Solve 12  –0.3p. Graph the solution set on a
number line.
Original inequality
Divide each side by –0.3,
reversing the inequality
symbol.
Simplify.
Rewrite with p first.
Solve an Inequality Using Multiplication
or Division
Answer: The solution set is p | p  –40.
A dot means that this
point is included in the
solution set.
What is the solution to –3x  21?
A. {x | x  –7}
B. {x | x  –7}
C. {x | x  7}
D. {x | x  7}
Solve Multi-Step Inequalities
Original inequality
Multiply each side by 2.
Add –x to each side.
Divide each side by –3,
reversing the inequality
symbol.
Solve Multi-Step Inequalities
A.
B.
C.
D.
Write and Solve an Inequality
CONSUMER COSTS Javier has at most $15.00 to
spend today. He buys a bag of pretzels and a bottle
of juice for $1.59. If gasoline at this store costs
$2.89 per gallon, how many gallons of gasoline,
to the nearest tenth of a gallon, can Javier buy for
his car?
Understand
Let g = the number of gallons of gasoline
that Javier buys. The total cost of the
gasoline is 2.89g. The cost of the
pretzels and juice plus the total cost of
the gasoline must be less than or equal
to $15.00.
Write and Solve an Inequality
Plan
Write an inequality.
The cost of
pretzels & juice
plus
1.59
+
the cost
of gasoline
2.89g
is less than
or equal to
$15.00.

15.00
Solve
Original inequality
Subtract 1.59 from
each side.
Simplify.
Write and Solve an Inequality
Divide each side
by 2.89.
Simplify.
Answer: Javier can buy up to 4.6 gallons of gasoline
for his car.
Check
Since
is actually greater than 4.6,
Javier will have enough money if he gets no
more than 4.6 gallons of gasoline.
RENTAL COSTS Jeb wants to rent a car for his
vacation. Value Cars rents cars for $25 per day plus
$0.25 per mile. How far can he drive for one day if
he wants to spend no more that $200 on car rental?
A. up to 700 miles
B. up to 800 miles
C. more than 700 miles
D. more than 800 miles