Download L1 – 2 Let`s Investigate A.REI.3 The following inequalities have been

L1 – 2
A.REI.3
Let’s Investigate
The following inequalities have been stumping professionals around you and they are seeking your
expert advice. Analyze the following inequalities and provide the requested information.
4𝑠 + 6 ≥ 6 + 4𝑠
3𝑟 + 5 > 3𝑟 − 2
4(𝑛 + 1) < 4𝑛 − 3
Do they have
solutions? If
so, what are
they?
Graph the
solutions on a
number line.
It is imperative for restaurants to consider food safety when serving their
customers. Food products must be held at certain temperatures to prohibit
the growth of bacteria. The thermometer on the left indicates different
temperature ranges in regards to food safety.
Graph the ideal temperature(s) for the growth of bacteria. Write an inequality
for this situation.
What would the graph look like for food safety? Write inequalities for this
situation.
How are the two graphs you just made different from the graphs in the chart?
L1 – 2
A.REI.3
Let’s Investigate
Below is a list of steps to solve compound inequalities. Fill in the justification for each step.
1.
Solve 3 < x – 6 < 9
Mathematical Computation
Justification
3 < x–6 < 9
Given
9 < x < 15
2.
Solve -5 < 4x + 7 < 12
Mathematical Computation
Justification
-5 < 4x + 7 < 15
Given
-12 < 4x < 8
-3 < x < 2
STOP to reflect!
What connection do you see between solving inequalities and solving compound inequalities?
_____________________________________________________________________________________
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Now try your hand at it.
3.
Solve -5 < 2x + 9 < 8 by listing your steps and providing your justification
Mathematical Computation
Justification
-5 < 2x + 9 < 8
Given
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A.REI.3
4.
Let’s Investigate
Solve 4 < 3x – 7 < 10 by listing your steps and providing your justification
Mathematical Computation
Justification
4 < 3x – 7 < 10
Given
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A.REI.3
Let’s Investigate
Answer Key
The following inequalities have been stumping professionals around you and they are seeking your
expert advice. Analyze the following inequalities and provide the requested information.
Do they have
solutions? If
so, what are
they?
4𝑠 + 6 ≥ 6 + 4𝑠
3𝑟 + 5 > 3𝑟 − 2
4(𝑛 + 1) < 4𝑛 − 3
Infinitely many
solutions
Infinitely many
solutions
No solution
Graph the
solutions on a
number line.
It is imperative for restaurants to consider food safety when serving their customers. Food products
must be held at certain temperatures to prohibit the growth of bacteria. The thermometer on the left
indicates different temperature ranges in regards to food safety.
Graph the ideal temperature(s) for the growth of bacteria. Write an inequality for this situation.
What would the graph look like for food safety? Write inequalities for this situation.
How are the two graphs you just made different from the graphs in the chart?
The chart illustrates infinitely many solutions by graphing with a line and no solutions by showing a
blank number line. The Food Safety graphs are showing specific boundaries by the use of segments and
rays.
Below is a list of steps to solve compound inequalities. Fill in the justification for each step.
L1 – 2
A.REI.3
1.
Let’s Investigate
Solve 3 < x – 6 < 9
Mathematical Computation
Justification
3 < x–6 < 9
Given
9 < x < 15
Addition Property
2.
Solve -5 < 4x + 7 < 12
Mathematical Computation
Justification
-5 < 4x + 7 < 15
Given
-12 < 4x < 8
Subtraction Property
-3 < x < 2
Division Property
STOP to reflect!
What connection do you see between solving inequalities and solving compound inequalities?
You still use the same algebraic properties when solving inequalities and compound inequalities. The
only difference when solving compound inequalities is that you have to remember to apply the algebraic
properties to ALL of the sides.
Now you try your hand at it:
3.
Solve -28 < 4(2x + 9) < 4 by listing your steps and providing your justification
Mathematical Computation
Justification
-28 < 4(2x + 9) < 4
Given
-28 < 8x + 36 < 4
Distributive Property
-64 < 8x < -32
Subtraction Property
-8 < x < -4
Division Property
L1 – 2
A.REI.3
4.
Let’s Investigate
Solve
Mathematical Computation
by listing your steps and providing your justification
Justification
Given
Multiplication Property
Addition Property
Division Property