Writing & Graphing Linear Inequalities

Writing & Graphing Linear Inequalities

MA.912. AR.2.6 - Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.

MA.912. AR.2.7 - Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.

MA.912. AR.2.8 - Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.

When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:

Fill in the Blank

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Multiple Choice

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

Which of the following inequalities would correctly represent the required length of the post?

• $$x\ \ge\ 5$$

• $$x\ \le\ 5$$

• $$x\ -\ 3\ \ge\ 5$$

• $$x\ +\ 3\le\ 5$$

Fill in the Blank

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Multiple Choice

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

Which inequality would help you solve this problem correctly?

• $$x\ +\ 14\ \le\ 35$$

• $$x\ +\ 14\ \ge35$$

• $$x\ -\ 14\ \ge35$$

• $$x\ -\ 14\ \le\ 35$$

Multiple Choice

You have $30 to buy baseball cards. Each pack of cards costs $5. Write an inequality that represents the number of packs of baseball cards you can buy and still have at least $10 left.

• $$30\ -\ 5x\ \ge10$$

• $$30\ -\ 5x\ \le\ 10$$

• $$30\ -\ 5x\ <\ 10$$

• $$30\ -\ 5x\ >\ 10$$

Multiple Choice

You have $30 to buy baseball cards. Each pack of cards costs $5. How many packs of baseball cards you can buy and still have at least $10 left?

• $$x\ \ge4$$

• $$x\ \le\ 4$$

• $$x\ <\ 4$$

• $$x\ >\ 4$$

Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

Multiple Choice

Graph the solution set of the inequality.

–4n + 1 > –23

Multiple Choice

What inequality does the number line graph represent?

• 2x +1 < -3

• x + 2 < 4

• -x + 3 > 1

• x + 4 >= 2

Graphing Linear Inequalities in two variables

Writing an Inequality in two-variables from a Graph

Multiple Choice

Which of the following inequalities matches the graph?

• y > x + 2

• y < -x + 2

• y < 2x + 2

• y < x + 2

Multiple Choice

Which of the following inequalities matches the graph?

• y < -4x - 1

• y < -(1/4)x - 1

• y < 4x - 1

• y < -4x - 1

Multiple Choice

Which of the following inequalities matches the graph?

• -2y > 2x - 2

• -2y > -4x + 4

• -2y < -4x + 4

• -2y ≤ 2x - 2

When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:

Multiple Choice

Aleris is sending a fancy organic fruit basket to her grandma for her birthday.  Apples cost $3 and oranges cost $2.  Aleris can spend no more than $24 on the gift.  
Write an inequality that describes the situation.
Let x = # of apples
Let y = # of oranges

• 3x + 2y < 24

• 3x + 2y > 24

• 3x + 2y ≤ 24

• 3x + 2y ≥ 24

Multiple Choice

In order to make some extra money, Justin is mowing lawns.  He charges $11 to mow a small lawn and $26 to mow a large lawn.  He would like to make at least $130.
Write an inequality that describes the situation.
Let x = # of small lawns mowed
Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y ≤ 130

• 11x + 26y > 130

• 11x + 26y < 130

Multiple Choice

Yumi is determining the seating arrangement for her big dinner party.  Circular tables will seat 8 guests and rectangular tables can seat 10 guests.  Together, all of the tables must seat at least 162 guests.
Write an inequality that describes the situation.
Let x = # of circular tables
Let y = # of rectangular tables

• 8x + 10y < 162

• 8x + 10y > 162

• 8x + 10y ≤ 162

• 8x + 10y ≥ 162