Linear Inequality Word Problems and Solutions with Two Variables

Which point below is NOT part of the solution set?

• (0, 0)
• (5, 1)
• (-1, -3)
• (20, -5)

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

How can I tell if an inequality will have a solid line?

• It has an equal sign.
• The symbol is greater than.
• The symbol has "or equal to."
• You just guess.

Will my line be solid?
5 ≥ x

• Yes
• No

Which point below is NOT a part of the solution set?

• (0, 0)
• (0, 1)
• (-100, -3)
• (5, 10)

What is the boundary line (symbol) of the graph?

• less than
• less than or equal to 
• greater than 
• greater than or equal to 

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

Which of the following is a linear inequality in two variables?

• 𝑥 + 𝑦 = 2

• 𝑥 + 5 > 8

• 3𝑚 + 5𝑛 < 10

• 3𝑞 – 2𝑞 ≠ 6

Which of the following inequalities illustrate “the sum of 𝑥 and 𝑦 is at most 15”?

• 𝑥 + 𝑦 = 15

• 𝑥 + 𝑦 > 15

• 𝑥 + 𝑦 ≤ 15

• 𝑥 + 𝑦 ≥ 15

Which of the following inequality has (5, 1) as a solution?

• 3𝑥 + 𝑦 ≤ 3

• 3𝑥 – 𝑦 ≤ 3

• 3𝑥 – 𝑦 < 15

• 3𝑥 + 𝑦 < 15