Unit 2 Test Review! . 7 th 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: . is less than. Fewer than, below. is greater than. More than, above.
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Unit 2 Test Review!
7th Grade Pre-Algebra
2013-2014
Ms. Beaty
An inequalitystates that two quantities
either are not equal or may not be
equal. An inequality uses one of the
following symbols:
is less than
Fewer than, below
is greater than
More than, above
is less than or equal to
At most, no more than
is greater than or equal to
At least, no less than
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.
x < 6
3 4 5 6 7 8 9 10
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 profitwas at least$20 higher thanJuly’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.
y
2
– 6 > 1
y
2
> 7
y
2
> (2)7
(2)
Additional Example 1A: Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
y
2
– 6 > 1
+ 6 + 6
Add 6 to both sides.
Multiply both sides by 2.
y > 14
Additional Example 1C: Solving Two-Step Inequalities
Solve.
4y – 5 < 11
4y – 5 < 11
+ 5 + 5
Add 5 to both sides.
4y < 16
4y < 16
Divide both sides by 4.
4
4
y < 4
12
252
, or 12
r ≤
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
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.
-7a -7a
-5a = 40
-5 -5
a = -8