3.05 Review: Identifying and writing inequalities
Identify the mathematical symbol \left( \lt, \gt, =\right) that makes each statement true:
\dfrac{2}{3} \enspace ⬚ \enspace 0.3
3.14 \enspace ⬚ \enspace \pi
12 \enspace ⬚ \enspace -12
\dfrac{1}{2} \enspace ⬚ \enspace 0.5
2.5 \enspace ⬚ \enspace 3
\dfrac{3}{20} \enspace ⬚ \enspace \dfrac{1}{11}
1.2 \enspace ⬚ \enspace \dfrac{6}{5}
-0.99 \enspace ⬚ \enspace -1
Write the following inequalities in words:
Write the inequality described by the following statements:
n is greater than 9.
n is greater than or equal to 9.
n is less than 10.
n is less than or equal to 6.
a is positive.
The product of 5 and x is less than or equal to - 20.
Seven more than the value of x is at least 9.
Eight is greater than the result of taking 7 away from x.
m can take the following set of values: 11, 10, 9, 8, 7, \ldots, and so on. Write an inequality that describes the set of values for m.
Write an inequality to represent each of the following situations:
The width of a particular road is 5 \text{ yd} or greater. Let w be the width of the road.
The elevator in a building should carry less than 13 people at one time. Let p be the number of people in the elevator.
Michael lives where it takes him at most 15 minutes to get to work. Let x be the time it takes Michael to get to work.
A building must be more than 160 \text{ m} tall to be considered a skyscraper. Let h be the height of the building.
The temperature inside a freezer is always below 0\degree \text{F}. Let T be the temperature inside the freezer.
In an amusement park, children below 5 years old can enter free of charge. Let c be the age of the a child that can enter the park free of charge.
Frasier is expecting that at least 50 guests will attend his party. Let g be the number of guests in Frasier's party.
In a gift exchange party, the attendees must spend at most \$ 50 on their gifts. Let x be the cost of a gift at the party.
Jack is saving up to buy a smartphone that is selling for \$510. He has \$210 in his bank account and expects some money for his birthday next week.
If the amount he is about to receive for his birthday is represented by x, write an inequality that models the situation where he is able to afford the smartphone.
Determine whether or not each of the following is a solution of k \leq 17:
k = - 17
k = 17
k = 16
k = 18
k = 25
k = -30
k = 10
k = -18
If x \leq - 4, find the largest integer value x can have.
If q \lt 0, find the largest integer value q can have.
If x > 15, find the smallest integer value x can have.
If n \geq 88, find the smallest integer value n can have.