ABSOLUTE VALUE OF INTEGERS WORKSHEET

Problem 1 :

Find the absolute value of the integer -9. 

Solution :

|-9|  =  9

Problem 2 : 

Find the absolute value of the integer 9. 

Solution :

|9|  =  9

Problem 3 : 

Find the absolute value of (-17 + 8). 

Solution :

|-17 + 8|  =  |-9|

|-17 + 8|  =  9

Problem 4 : 

Find the absolute value of (28 - 13).

4. Answer :

|28 - 13|  =  |15|

|28 - 13|  =  15

Problem 5 : 

If |x| is an integer between 0 and 3, then, find all possible values of x. 

Solution :

Given : |x| is an integer between 0 and 3. 

Then, we have

|x|  =  1  and  |x|  =  2

Solve for x in |x|  =  1. 

Solve for x in |x|  =  2. 

So, the possible values of x are 

-2, -1, 1, 2

Problem 6 :

If |2x - 1| is an integer between 3 and 6, then, find all possible values of x. 

Solution :

Given : |2x - 1| is an integer between 3 and 6. 

Then, we have

|2x - 1|  =  4  and  |2x - 1|  =  5

Solve for x in |2x - 1|  =  4. 

Solve for x in |2x - 1|  =  5. 

So, the possible values of x are 

-2, -3/2, 5/2, 3

Problem 7 :

Solve for x : 

|3x + 5|  =  7

Solution :

|3x + 5|  =  7

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-4, 2/3

Problem 8 :

Solve for x : 

|7x|  =  21

Solution :

|7x|  =  21

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-3, 3 

Problem 9 :

Solve for x :

2|3x +4|  =  8

Solution :

2|3x +4|  =  7

Divide each side by 2. 

|3x + 4|  =  4

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-8/3, 0

Problem 10 :

Solve for x : 

3|5x - 6| - 4  =  5

Solution :

3|5x - 6| - 4  =  5

Add 4 to each side.

3|5x - 6|  =  9

Divide each side by 3.

|5x - 6|  =  3

So, the values of x are 

3/5, 9/5

Problem 10 :

g(x) = |(7/9) x - 40|

The function g is defined by the given equation. For which of the following values of a does g(a) = a ?

a) -180    b)  27/2   c) 45/2   d) 360/7

Solution :

g(x) = |(7/9) x - 40|

g(a) = |(7/9) a - 40|

a = |(7/9) a - 40|

From the options given -180 is the answer.

Problem 11 :

|x - 13| = |x + 5|

What is the solution to the given equation

a) -8    b)  -4   c)  4   d)  8

Solution :

|x - 13| = |x + 5|

x - 13 = x + 5 or x - 13 = -(x + 5)

x - x = 5 + 13

no solution from this branch.

x - 13 = -x - 5

x + x = -5 + 13

2x = 8

x = 4

So, the value of x is 4.

Problem 12 :

The number of boats B a boat dealer sells in each month of the year from March to December can be modeled by the function

𝐵 = −15|t − 5| + 120

where t is the time in months and t = 1 represents January.

a] Complete the table of values and then graph the function

b) What is the maximum number of sales in one month?

c) In what month is the maximum reached?

d) What is the minimum number of sales in one month?

e] In what month is the minimum reached?

Solution :

𝐵 = −15|t − 5| + 120

(3, 90)(5, 120) (7, 90) (9, 60) (11, 30) (12, 15)

b) The maximum number of sales = 120

c) The maximum number of sales in the month of May.

d) The minimum number of sales is 15.

e] In the month of december.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.