Transcript less than - Ms. Beaty`s 7th Grade Math Class

Unit 2 Test
Review!
7th Grade Pre-Algebra
2013-2014
Ms. Beaty
An inequality states that two quantities
either are not equal or may not be
equal. An inequality uses one of the
following symbols:
Symbol
<
>
Meaning
Word Phrases
is less than
Fewer than, below
More than, above
≤
is greater than
is less than or
equal to
≥
is greater than
or equal to
At least, no less than
At most, no more than
Graphing inequalities

When a number is greater than or less than,
you used an open dot on the graph.


I think of the dot as being empty. It does not
contain the number it is on.
When a number is greater than or equal to or
less than or equal to, you use a closed dot.

I think of the dot as being full. It contains the
number it is on.
Let’s try one!!!
3+x<9
WAIT!
The x is not isolated yet! What do we do??
That’s right! We do the inverse to isolate the
variable. It’s the same way you have
been solving the equations.
Let’s try it again!

3+x<9

Isolate the variable by undoing the constant.
Subtract 3 from both sides and you’re left with:
x<6

This would read x is less than 6. This means that x
can be any number less than 6.

In order to represent this, we put it on a graph.
Graphing the inequality
x
<6
3
4
5
6
7
8
9
10
 Why
did we use an open dot?
 Why
did the arrow point to the left?
Let’s try a few more!
X
> 4.5
X
< -3
X
< -17
X
>4
Lets try inequalities with words!
 All
real numbers less than 5
 All
real numbers greater than -1
 All
real number less than or equal to ½
 All
real number greater than or equal to 0
Write an inequality for the situation.
There are at most 87 people in the school.
Write an inequality for the situation.
At least 31 pencils are on the tray.
Additional Example 3: Money Application
Edgar’s August profit of $137 was at least $20
higher than his July profit. What was July’s
profit?
Let p represent the profit increase from July to
August.
August profit was at least $20 higher than July’s profit.
$137
≥
20
+
p
137 ≥ 20 + p
Subtract 20 from both sides.
-20 -20
117 ≥ p
p ≤ 117
Rewrite the inequality.
July’s profit was at most $117.
 Antonio
has read at least 12 more books
than Benji. If Benji has read 32 books, at
least how many books has Antonio read?
Additional Example 1A: Solving Two-Step
Inequalities
Solve. Then graph the solution set on a
number line.
y
2 –6>1
y
2 –6>1
+6 +6
Add 6 to both sides.
y
>7
2
y > (2)7
Multiply both sides by 2.
(2) 2
y > 14
Additional Example 1C: Solving Two-Step
Inequalities
Solve.
4y – 5 < 11
4y – 5 < 11
+5 +5
4y
< 16
4y
< 16
4
4
y<4
Add 5 to both sides.
Divide both sides by 4.
Additional Example 2: Application
Sun-Li has $30 to spend at the carnival.
Admission is $5, and each ride costs $2. What
is the greatest number of rides she can ride?
Let r represent the number of rides Sun-Li can ride.
5 + 2r ≤ 30
–5
–5
Subtract 5 from both sides.
2r ≤ 25
Divide both sides by 2.
2r ≤ 25
2
2
1
r ≤ 25 , or 12
2
2
Sun-Li can ride only a whole number of rides, so the
most she can ride is 12.
Check It Out: Example 2
Brice has $30 to take his brother and his friends
to the movies. If each ticket costs $4.00, and he
must buy tickets for himself and his brother,
what is the greatest number of friends he can
invite?
Let t represent the number of tickets.
8 + 4t ≤ 30
–8
–8
Subtract 8 from both sides.
4t ≤ 22
Divide both sides by 4.
4t ≤ 22
4
4
t ≤ 5.5
Brice can only buy a whole number of tickets, so the
most people he can invite is 5.
Combining Like Terms
 Must


have the same:
Variable (Letter)
Exponent (Power)
 Example:
 (2a
+ 3) + (a +7)
Steps for Solving a 2-Step
Equation.
 Our
Goal: Isolate the Variable!

1. Draw your slide to line up the equal signs.

2. Undo the constant by using the inverse
operation.
3. Undo the variable term by using the
inverse operation
4. Write the solution.


4x + 2 = 38
What if there are two variable
terms?
 2a
= 7a +40
-7a -7a
-5a = 40
-5
-5
a = -8
 1.
Get the variable
terms on one side,
and constants on
the other.
 Use inverse
operation to isolate
the variable.
Words in Math
addition
• Add
• And
• Plus
• More than
• Sum
• All together
• combine
Subtraction
• Less than
• Minus
• Take away
• Difference
• Subtract
• Deduct
• Discount
Multiplication
• Times
• Double
• Triple
• Multiply by
• Product
• Of
• Per
Division
• Goes into
• Divided by
• Divided into
• Quotient
• Per
Equations
Inequalities
• Equals
• Is
• Is equal to
•=
• Is less than <
• Is fewer than <
• Is more than >
• Is greater than >
Look for key words and
translate them into
mathematic symbols.
 Special
cases

More than : addition expression with the
terms swapped

Less than: subtraction expression with the
terms swapped

Divided into: division expression with the
terms swapped
 Luis’s
cell phone plan costs $39 per
month. Text messages cost an additional
$0.15 each. If Luis’s cell phone bill last
month totaled $55.05, write and solve an
equation to determine how many text
messages he sent.
 Syreeta
wants to buy some CDs that each
cost $23. She has $65. Write and solve an
equation to find how many CDs she can
buy.
 Toya
had her birthday party at the
movies. IT cost $27 for pizza and $8.50 per
friend for the movie tickets. How many
friends did Toya have at her party if she
spent $78.
 Joan
bought a soft drink for 2 dollars and
7 candy bars. She spent a total of 16
dollars. How much did each candy bar
cost?
 Oceanside
Bike Rental Shop charges 11
dollars plus 7 dollars an hour for renting a
bike. Keith paid 53 dollars to rent a bike.
How many hours did he pay to have the
bike checked out?
 Liam
bought a movie ticket and a
popcorn for $24. What was the price of
each item if the ticket cost 3 times as
much as the popcorn?
 Doritos
are on sale at Kroger. If Ms. Beaty
buys 3 bags, it will cost her $6. If she buys
them individually, she has to pay $3.99
each. How much money will she save on
each bag if she buys 3.
 Ms.
Beaty can buy a Blu-Ray player for
$45 and rent redbox movies for $10 a
month or she can use her laptop and
stream netflix for $15 per month. How
many months would she need to stream
netflix to pay as much as she would if she
had bought the Ble-Ray and rented
redbox movies?
 One
movie ticket at the Mall of Georgia
costs $18, while one movie ticket at Regal
costs $12. What is the difference in cost if
you buy 5 tickets at each theater?
 Jackie
visited New York City and needed
to take a cab from the airport to her
hotel. The cab charges a $5.00 fee plus
$0.20 per mile. If her total cost was $9.80,
how many miles did Jackie ride in the
cab?
 Kristina
rented a car for a road trip. She
paid a rental fee of $60.00, as well as
$9.75 each day. Her total cost was
$138.00. For how many days did she rent
the car?
 Ms.
Beaty found a Braves shirt that she
wants to buy for her little brother’s
birthday. The original price is $25. It is
currently on sale at 15% off Ms. Beaty also
has a $5 coupon. How much will the shirt
cost before tax?
 Yuan
just bought a new television for
$719.00. He made a down payment of
$68.00 and will pay monthly payments of
$31.00 until it is paid off. How many
months will Yuan be paying? (Assume that
Yuan pays no interest.)
A
store is selling a couch for $873.00 on a
24-month payment plan. If a down
payment of $121.00 is given, and no
interest is charged, how much will a
customer have to pay each month?
Round your answer to the nearest cent.
 Taylor
needs to take a taxi to get to the
movies. The taxi charges $4.00 for the first
mile, and then $3.00 for each mile after
that. If the total charge is $17.50, then
how far was Taylor’s taxi ride to the
movie?
 Monday's
low temperature in New York
was 30°F. The same day in Dallas, the low
temperature was above 57°F. at least
how many degrees warmer was the low
temperature in Dallas than the low in New
York?
 Erin
spent $12.25 on supplies to make
lemonade. At least how many glasses of
lemonade must she sell at $0.30 per glass
to make a profit?
 Greg
has $357.00. A DVD player costs
$114.00, and he can purchase used
movies for $8.85 each. What is the
greatest number of movies Greg can buy
if he also buys a DVD player?