GRAPHING AND WRITING INEQUALITIES WORKSHEET

Problem 1 :

Describe the solutions of 3 + x < 9 in words.

Problem 2 :

Describe the solutions of 2y > 4 in words.

Problem 3 :

Graph :

x < -1.5

Problem 4 :

Graph :

y ≥ 2

Problem 5 :

Graph :

2² - 4 ≥ z

Problem 6 :

Write the inequality for the graph shown below.

Problem 7 :

Write the inequality for the graph shown below.

Problem 8 :

Write the inequality for the graph shown below.

Problem 9 :

The members of a lightweight crew team can weigh no more than 165 pounds each. Define a variable and write an inequality for the acceptable weights of the team members. Graph the solutions.

Problem 10 :

A store’s employees earn at least $8 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

Answers

1. Answer :

Test values of x that are negative, 0 and positive.

When the value of x is a number less than 6, the value of 3 + x is less than 9.

When the value of x is 6, the value of 3 + x is equal to 9.

When the value of x is a number greater than 6, the value of 3 + x is greater than 9.

The solutions of 3 + x < 9 are numbers less than 6.

2. Answer :

Test values of y that are negative, 0 and positive.

When y = -1,

2(-1) > 4 -----> -2 > 4 (false, -1 is not a solution)

When y = 0,

2(0) > 4 -----> 0 > 4 (false, 0 is not a solution)

When y = 1,

2(1) > 4 -----> 2 > 4 (false, 1 is not a solution)

When y = 2,

2(2) > 4 -----> 4 > 4 (false, 2 is not a solution)

When y = 3,

2(3) > 8 -----> 6 > 4 (true, 3 is a solution)

When y = 4,

2(4) > 8 -----> 8 > 4 (true, 4 is a solution)

When y = 5,

2(5) > 8 -----> 10 > 4 (true, 5 is a solution)

When the value of y is a number less than 2, the value of 2y is less than 4.

When the value of y is 2, the value of 2y is equal to 4.

When the value of y is a number greater than 2, the value of 2y is greater than 4.

The solutions of 2y are numbers greater than 2.

3. Answer :

Draw an empty circle at -1.5.

Shade all the numbers less than -1.5 and draw an arrow pointing to the left.

4. Answer :

Draw a solid circle at 2.

Shade all the numbers greater than 2 and draw an arrow pointing to the right.

5. Answer :

2² - 4 ≥ z

Simplify. 

4 - 4 ≥ z

0 ≥ z

z ≤ 0

Draw a solid circle at 0.

Shade all the numbers less than 0 and draw an arrow pointing to the left.

6. Answer :

Use any variable. The arrow points to the right, so use either > or ≥. The empty circle at 4.5 means that 4.5 is not a solution, so use >.

x > 4.5

7. Answer :

Use any variable. The arrow points to the left, so use either < or ≤. The solid circle at -3 means that -3 is a solution, so use ≤.

y ≤ -3

8. Answer :

Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2.5 means that 2.5 is not a solution, so use <.

z < 2.5

9. Answer :

Let w represent the weights that are allowed.

w ≤ 165

Stop the graph at 0 because a person’s weight must be a positive number.

10. Answer :

Let e represent the employees earning.

e ≥ 8

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.