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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
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.
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
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
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
Then check your solution.
Original inequality
Subtract 13 from each side.
Simplify.
Divide each side by –11 andchange
Simplify.
Inequality Involving a Negative Coefficient
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
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
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
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
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
Solving Multi-Step Inequalities
When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols.
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
Answer: Since is the same as
the solution set is
Distributive Property
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
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.
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
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
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