Download Solve Multi-Step Inequalities

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.
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
Solve the equation |b + 20| = 21.
A. {–41, 1}
B. {–41, –1}
C. {–1, 1}
D. {1, 2}
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
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.
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