Intro to Linear Inequalities

Intro to Linear Inequalities

Multiple Choice

If the inequality symbol is  $$<$$  or  $$>$$ , the line will be _________.

• solid

• dotted

Multiple Choice

If the inequality symbol is  $$\le$$   or  $$\ge$$ , the line will be  ___________.

• solid

• dotted

Multiple Choice

Slope is describe as

• $$\frac{rise}{run}$$  

• $$\frac{run}{rise}$$  

Multiple Choice

Which of the following is true of the given graph?

y ≥ -2x + 1

• The graph is a dotted line, shaded above.

• The graph is a solid line, shaded above.

• The graph is a dotted line, shaded below.

• The graph is a solid line, shaded below.

Multiple Choice

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set
• No, they are NOT part of the solution set

Multiple Choice

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

• Yes because it is located in the shaded region.

• No because it is located on the line and the line is dotted.

• Yes because it is located on the line.

• No because it is in the shaded region.

Multiple Select

When graphing $$y<\frac{3}{5}x-4$$  , you will draw which of the following.

• A dotted line

• A solid line

• Shade up

• Shade down

Multiple Select

When graphing $$y\ge-\frac{2}{7}x+1$$  , you will draw which of the following.

• A dotted line

• A solid line

• Shade up

• Shade down

Multiple Choice

Which of the following is "NOT" a solution for the inequality?

y ≤ 5x - 1

• (0, -3)

• (5, 24)

• (-2, -15)

• (1, 7)

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Which of the following equations match the given graph?

• y  < 2/5x + 1
• y ≥ -2/5x + 1
• y ≤  2/5x + 1
• y ≥ -2/5x - 1

Multiple Select

According to the graph, which point is a solution? Choose all that apply.

• (0, 0)

• (4, 2)

• (-1, -5)

• (-3, 0)

Multiple Choice

This is a graph of which inequality?

• y > 4x - 2

• y > -2x + 4

• y < -2x

• y < 4X - 2

Multiple Choice

Which inequality below is equivalent to

3x - y > 4

• y > 3x - 4

• y < -3x + 4

• y < 3x - 4

• y > -3x + 4

Multiple Choice

Which of the following is the graph of

3x - 2y < 10

Math Response

Write the equation of the linear inequality in slope-intercept form.

Type answer here

Correct Answer: y>x-2

Deg^°

Rad

Math Response

Write the equation of the linear inequality in slope-intercept form.

Type answer here

Correct Answer: y\le\frac{3}{2}x+3

Deg^°

Rad

Draw

Graph the following inequality:

$$y<\frac{1}{2}x-8$$

Draw

Graph the following inequality:

$$y\ge-x$$

Multiple Choice

Addie saved more than $36. Which inequality represents the amount that she saved? 

• s > 36
• s < 36
• s ≤ 36
• s ≥ 36

Multiple Choice

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike? 

• 15h ≤ 105
• 15h > 105
• 15h < 105
• 15h ≥ 105

Multiple Choice

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600
• 125x + 55 ≥ 600
• 125x + 55 > 600
• 125x + 55 < 600

Multiple Choice

The Bombetta Company wants to send a team of three representatives to a conference.  Their budget is $700.00 plus $125.00 per day for expenses.  If their total budget cannot exceed $1,400.00, which of the following inequalities expresses this situation?

• 125x + 700 ≥1,400
• 700 + 125x ≤1,400
• 700x + 125 ≤1,400
• 125x - 700 ≤ 1,400

Multiple Choice

The Bombetta Company wants to send a team of three representatives to a conference.  Their budget is $700.00 plus $125.00 per day for expenses.  If their total budget cannot exceed $1,400.00, which of the following inequalities expresses this situation?

• 125x + 700 ≥1,400
• 700 + 125x ≤1,400
• 700x + 125 ≤1,400
• 125x - 700 ≤ 1,400

Multiple Choice

The Bombetta Company wants to send a team of three representatives to a conference.  Their budget is $700.00 plus $125.00 per day for expenses.  If their total budget cannot exceed $1,400.00, which of the following inequalities expresses this situation?

• 125x + 700 ≥1,400
• 700 + 125x ≤1,400
• 700x + 125 ≤1,400
• 125x - 700 ≤ 1,400

Multiple Choice

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each.  Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 150c + 325d < 6,500
• 325c + 150d <6,500
• 150c + 325d ≤ 6,500
• 325c + 150d ≤ 6,500

Multiple Choice

A donut shop charges $0.70 for each donut and $0.30 for a carryout box.  Shirley has $5.00 to spend.  She needs to determine the most donuts (x) she can buy when she only puts them in one carryout box.  Which equation can be used to answer this problem?

• 70x + 30 < 500
• 30x + 70 < 500
• 70x + 30 ≤500
• 30x + 70 ≤ 500

Multiple Choice

Gideon needs to collect at least 1,000 signatures for a petition to free all Koalas from zoos. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which inequality represents this situation?

• $$520x+6\le1000$$  

• $$520+6x\ge1000$$  

• $$520x+6\ge1000$$  

• $$520+6x\le1000$$  

Multiple Choice

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Multiple Choice

Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.

Which inequality could help you find how many dogs Katie would have to walk to reach her goal?

• 25 - 12x ≥ 200

• 25 + 12x ≥ 200

• 13x ≥ 200

• 25 + 12x < 200

Multiple Choice

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

• 6x + 8 ≥ 42

• 8x + 6 ≤ 42

• 6x + 8 > 42

• 8x + 6 < 42

Multiple Choice

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn.

Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100