GRAPH INEQUALITIES ON A NUMBER LINE WORKSHEET

Solve the inequalities and represent the possible values of the variable on a number line.

1)  6 > z - 2

2)  g + 7 < -12

3)  d – 5 < 7

4)  15 > k + 2

5)  1 + x > -16

6)  y + 8 < -9

7)  8 ≤ 8 + r

8)  w + 8 ≥ 11

Solution

Problem 9 :

The NASA Solar Probe can withstand temperatures up to and including 2600°F. Write and graph an inequality that represents the temperatures the probe can withstand.

Solution

Problem 10 :

Describe and correct the error in graphing the inequality.

Solution

Problem 11 :

Describe and correct the error in graphing the inequality.

Solution

Problem 12 :

Each day at lunchtime, at least 53 people buy food from a food truck. Write an inequality that represents this situation.

Solution

Problem 13 :

A subway ride for a student costs $1.25. A monthly pass costs $35.

a. Write an inequality that represents the number of times you must ride the subway for the monthly pass to be a better deal.

b. You ride the subway about 45 times per month. Should you buy the monthly pass? Explain.

Solution

Problem 14 :

Consider the inequality b > − 2.

a. Describe the values of b that are solutions of the inequality.

b. Describe the values of b that are not solutions of the inequality. Write an inequality for these values.

c. What do all the values in parts (a) and (b) represent? Is this true for any inequality?

Solution

Problem 15 :

A postal service says that a rectangular package can have a maximum combined length and girth of 108 inches. The girth of a package is the distance around the perimeter of a face that does not include the length.

a. Write an inequality that represents the allowable dimensions for the package.

b. Find three different sets of allowable dimensions that are reasonable for the package. Find the volume of each package.

Solution

Answer Key

1)  z < 8

2)  g < -19

3)  d < 12

4)  k < 13

5)  x > -17

6)  y < -17

7)  r ≥ 0

8)  w ≥ 3

9)  t ≤ 2600

10) The error is, the circle should be closed circle.

11) The circle should be open circle.

12) x ≥ 53 (at least)

13) a) the minimum number of times the monthly pass t be used is 28.

b) Since the amount what we receive is greater than 35, we should purchase monthly pass to reduce expenses.

14) 

a) Given that, b > − 2

The values of b should be greater than -2.

b) The values of b should be lesser than -2 including -2.

c)  These values represent all real numbers. This is true for any inequality because every real number is either a solution or it is not.

15) a) l + 2w + 2h ≤ 108

b)  4800 cubic inches,  4500 cubic inches and 3600 cubic inches

Solve each inequality.

Problem 1 :

4x - 1 ≥ 7

Solution

Problem 2 :

2(x – 5) ≤ 8

Solution

Problem 3 :

3 – 2x < x + 6

Solution

Problem 4 :

(1/2)x > 5

Solution

Problem 5 :

3(x + 4) > 12

Solution

Problem 6 :

2x – 7 ≤ 5 – 4x

Solution

Problem 7 :

3x + 2 < 11

Solution

Problem 8 :

4(x – 6) ≥ 20

Solution

Problem 9 :

(1/4)x < 2

Solution

Problem 10 :

12 – 3x > 2x + 1

Solution

Problem 11 :

(x – 5)/7 ≤ -3

Solution

Problem 12 :

3(5 – x) ≥ 7x - 1

Solution

Problem 13 :

3y – (2y + 2) ≤ 7

Solution

Problem 14 :

(m + 2)/5 < 2m/3

Solution

Problem 15 :

(m – 2)/3 ≥ (2m + 1)/7

Solution

Draw a number line graph of:

Problem 1 :

{x│-2 ≤ x ≤ 3}

Solution

Problem 2 :

{x│0 < x < 3}

Solution

Problem 3 :

{x │ x < 1  or x > 3}

Solution

Problem 4 :

{x│ x ≤ 2 or x ≥ 3}

Solution

Problem 5 :

{x│ x ≤ -2 or x > 1}

Solution

Problem 6 :

{x│-1 < x ≤ 4}

Solution

Problem 7 :

{x│ -3 ≤ x < 0}

Solution

Problem 8 :

{x│ x < 0 or x ≥ 4}

Solution

Problem 9 :

{x│ x ≤ -1 or 0 ≤ x ≤ 3}

Solution

Problem 10 :

{x│ -2 ≤ x ≤ 2 or x ≥ 4}

Solution

Problem 11 :

Write the sentence as an inequality. 

a)  A number x is greater than 3.

b)   A number n plus 7 is less than or equal to 9.

c) Fifteen is no more than a number t divided by 5.

d) Three times a number w is less than 18

e)  One-half of a number y is more than 22.

f)  Three is less than the sum of a number s and 4.

g)  Thirteen is at least the difference of a number v and 1.

h)  Four is no less than the quotient of a number x and 2.1

Solution

Problem 12 :

The winner of a weight-lifting competition bench-pressed 400 pounds. The other competitors all bench-pressed at least 23 pounds less.

a. Write an inequality that represents the weights that the other competitors bench-pressed.

b. Was one of the other competitors able to bench-press 379 pounds? Explain.

Solution

Answer Key

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11) a) x > 3

b) n + 7 ≤ 9

c) 15 ≤ t/5

d) 3w < 18

e) y/2 < 22

f) 3 < s + 4

g) 13 > v - 1

h) 4 < x/2.1

12)  a) 377 pounds

b)  weight is outside the range of possible weights for the other competitors. 

Related Pages

• How to plot inequalities on the number line
• Solving inequalities by multiplying or dividing
• Graphing the inequality on the number line
• Solving quadratic inequalities
  
• Solving rational inequalities
• Examples of solving rational inequalities
• Graphing systems of inequalities
• Word problems equations and inequalities
• Solving inequalities by clearing fractions
• Translating phrase into equations and inequalities
• Solving absolute value inequalities