math pacing solving multi-step inequalities solve each inequality. 1.2. 3. which inequality is not...
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Solving Multi-Step Inequalities
Solve each inequality.
1. 2.
3. Which inequality is not represented by the graph:
1089 v9
5
3
2
c
12| vv
6
5| cc
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Solving Multi-Step Inequalities
Solving inequalities involving more than one operation can be solved by undoing the operations in the same way you would solve an equation with more than one step.
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Science The inequality F > 212 represents the
temperatures in degrees Fahrenheit for which water is
a gas (steam). Similarly, the inequality
represents the temperatures in degrees Celsius for
which water is a gas. Find the temperature in degrees
Celsius for which water is a gas.
Solve a Real-World Problem
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Answer: Water will be a gas for all temperaturesgreater than 100°C.
Original inequality
Subtract 32 from each side.
Simplify.
Multiply each side by
Simplify.
Solve a Real-World Problem
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Science The boiling point of helium is –452°F. Solve
the inequality to find the temperatures
in degrees Celsius for which helium is a gas.
Answer: Helium will be a gas for all temperatures greater than –268.9°C.
Solve a Real-World Problem
Do this one in your notes, please!
48459 C Subtract 32 from each side
48495 C Multiply each side by 5/9
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Then check your solution.
Original inequality
Subtract 13 from each side.
Simplify.
Divide each side by –11 andchange
Simplify.
Inequality Involving a Negative Coefficient
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Check To check the solution, substitute –6, a number less than –6, and a number greater than –6.
Answer: The solution set is
Inequality Involving a Negative Coefficient
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Then check your solution.
Answer:
Inequality Involving a Negative Coefficient
Do this one in your notes, please!
88 y
1y
Subtract 3 from each side
Divide each side by – 8
AND reverse the inequality
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Write an inequality for the sentence below. Then solve the inequality.
Four times a number plus twelve is less than a number minus three.
Four timesa number plus
is less than
a numberminus three. twelve
4n + <12
Write and Solve an Inequality
Let n = a number
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Original inequality
Subtract n from each side.
Simplify.
Subtract 12 from each side.
Simplify.
Divide each side by 3.
Simplify.
Answer: The solution set is
Write and Solve an Inequality
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Write an inequality for the sentence below. Then solve the inequality.
6 times a number is greater than 4 times the number minus 2.
Answer:
Write and Solve an Inequality
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Solving Multi-Step Inequalities
When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols.
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Original inequality
Add c to each side.Simplify.Subtract 6 from each side.Simplify.
Divide each side by 4.
Simplify.
Combine like terms.Distributive Property
Distributive Property
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Answer: Since is the same as
the solution set is
Distributive Property
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Answer:
Distributive Property
Do this one in your notes, please!
pppp 32823 248 pp
238 p Subtract p from each side
Distributive Property
Combine like terms
p310 Add 2 to each side
Divide each side by 3
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Solving Multi-Step Inequalities
If solving an inequality results in a statement that is always true, the solution is all real numbers.
If solving an inequality results in a statement that is never true, the solution is the empty set . The empty set has no members.
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Answer: Since the inequality results in a falsestatement, the solution set is the empty set Ø.
Original inequality
Distributive Property
Combine like terms.
Subtract 4s from each side.
This statement is false.
Empty Set
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Answer: Ø
Empty Set
Do this one in your notes, please!
rrrr 587264 8262 rr
86 This statement is false.
Distributive Property
Combine like terms