HOW TO PLOT INEQUALITIES ON A NUMBER LINE

Draw a number line graph of:

Problem 1 :

{x│-2 ≤ x ≤ 3}

Solution :

 -2 ≤ x ≤ 3

Since the given inequalities -2 ≤ x ≤ 3 (less than or equal and less than or equal), we draw the line from -2 with a filled circle to 3 with a filled circle on the number line.

Problem 2 :

{x│0 < x < 3}

Solution :

Since the given inequalities 0 < x < 3 (less than and less than), we draw the line from 0 with an unfilled circle to 3 with an unfilled circle on the number line.

Problem 3 :

{x │ x < 1  or x > 3}

Solution :

Given, x < 1 or x > 3 is a compound inequality OR.

Since the first inequality x < 1 (less than), so we draw the line left side from 1 with an unfilled circle on the number line.

Since the second inequality x > 3(greater than), so we draw the line right side from 3 with an unfilled circle on the number line.

Problem 4 :

{x│ x ≤ 2 or x ≥ 3}

Solution :

Given, x ≤ 2 or x ≥ 3 is a compound inequality OR.

Since the first inequality x ≤ 2 (less than or equal), so we draw the line left side from 2 with a filled circle on the number line.

Since the second inequality x ≥ 3(greater than or equal), so we draw the line right side from 3 with a filled circle on the number line.

Problem 5 :

{x│ x ≤ -2 or x > 1}

Solution :

Given, x ≤ -2 or x > 1 is a compound inequality OR.

Since the first inequality x ≤ -2 (less than or equal), so we draw the line left side from 2 with a filled circle on the number line.

Since the second inequality x > 1(greater than), so we draw the line right side from 1 with an unfilled circle on the number line.

Problem 6 :

{x│-1 < x ≤ 4}

Solution :

Since the given inequalities -1 < x ≤ 4 (less than and less than or equal), we draw the line from -1 with an unfilled circle to 4 with a filled circle on the number line.

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 :

a)  A number x is greater than 3.

x > 3

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

n + 7 ≤ 9

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

15 ≤ t/5

d) Three times a number w is less than 18

3w < 18

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

1/2 of y < 22

y/2 < 22

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

3 < s + 4

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

13 > v - 1

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

4 < x/2.1

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 :

Weight lifted by winner = 400 pounds

The other competitor pressed at least 23 pounds less

a)  The competitor bench presses that weights 400 - 23 ==> 377 pounds

If w represents the weight in pounds lifted by another competitor, the condition is represented by the inequality:

w ≤ 377

b)  No, one of the other competitors was not able to bench-press 379 pounds. 

According to the inequality w≤377w is less than or equal to 377𝑤≤377 derived from the problem's conditions, all other competitors lifted a weight less than or equal to 377 pounds. Since 379>377. 379 is greater than 377379>377, this weight is outside the range of possible weights for the other competitors.