Transcript Interactive Chalkboard

B5
Solving Linear Inequalities
Example 1 Solve an Inequality Using Addition
or Subtraction
Example 2 Solve an Inequality Using Multiplication
or Division
Example 3 Solve a Multi-Step Inequality
Example 4 Write an Inequality
Solve
number line.
Graph the solution set on a
Original inequality
Subtract 4y from each side.
Simplify.
Subtract 2 from each side.
Simplify.
Rewrite with y first.
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.
Solve
number line.
Answer:
Graph the solution set on a
Solve
number line.
Graph the solution set on a
Original inequality
Divide each side by –0.3,
reversing the inequality symbol.
–40  p
p  –40
Simplify.
Rewrite with p first.
Answer: The solution set is
A dot means that this
point is included in the
solution set.
Solve
number line.
Answer:
Graph the solution set on a
Solve
Graph the solution set on a
number line.
Original inequality
Multiply each side by 2.
Add –x to each side.
Divide each side by –3,
reversing the inequality symbol.
Answer: The solution set is
graphed below.
and is
Solve
number line.
Answer:
Graph the solution set on a
Consumer Costs Alida has at most $10.50 to
spend at a convenience store. She buys a bag of
potato chips and a can of soda for $1.55. If gasoline
at this store costs $1.35 per gallon, how many
gallons of gasoline can Alida buy for her car, to the
nearest tenth of a gallon?
Explore Let
the number of gallons of gasoline that
Alida buys.
Plan
The total cost of the gasoline is 1.35g. The cost
of the chips and soda plus the total cost of the
gasoline must be less than or equal to $10.50.
Write an inequality.
The cost of
chips & soda
1.55
Solve
plus
the cost
of gasoline
is less than
or equal to
$10.50.
+
1.35g

10.50
Original inequality
Subtract 1.55
from each side.
Simplify.
Divide each side
by 1.35.
Simplify.
Answer: Alida can buy up to 6.6 gallons of gasoline for
her car.
Examine Since
is actually greater than 6.6, Alida
will have enough money if she gets no more
than 6.6 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?
Answer: up to 700 miles