Integers and absolute value worksheet is much useful to the kids who would like to practice problems on absolute value and absolute value equations.

**Please click here to download "Solving absolute value equations pdf"**

Before we look at integers and absolute value worksheet, let us look at some basic stuff about solving absolute value equations.

"Solving absolute value equations" is the stuff which is being studied by the students who study high school math.

Here we are going to see, "How to solve an absolute value equation"

And do remember, before solving any absolute value function, it has to be in the form of **|x + a| = k **(There should be only absolute part on the left side)

(Here "a" and "k" are real numbers)

Let us consider the absolute value equation |2x + 3| = 5.

The picture given below clearly explains, "How the above absolute value equation can be solved".

1) Solve the absolute value function |3x + 5| = 7

2) Solve the absolute value function |7x| = 21

3) Solve the absolute value function |2x + 5| + 6 = 7

4) Solve the absolute value function |x - 3| + 6 = 6

5) Solve the absolute value function 2|3x +4| = 7

6) Solve the absolute value function 3|5x - 6|- 4 = 5

7) Solve the absolute value function |x² - 4x - 5| = 7

8) Solve the absolute value function 0.5|0.5x| - 0.5 = 2.5

9) If the absolute value equation |2x+k| = 3 has the solution x = -2, find the value of "k".

10) If the absolute value equation |x - 3| - k = 0 has the solution x = -5, find the value of "k".

**Problem 1 :**

Solve the absolute value function |3x + 5| = 7

**Solution :**

When we apply the method explained above for |3x + 5| = 7,

we get 3x + 5 = 7 or 3x + 5 = -7

3x = 2 or 3x = -12

x = 2/3 or x = -4

**Hence the solution is x = -4, 2/3**

Let us look at the next problem on "Integers and absolute value worksheet".

**Problem 2 :**

Solve the absolute value function |7x| = 21

**Solution :**

When we apply the method explained above for |7x| = 21,

we get 7x = 21 or 7x = -21

x = 3 or x = -3

**Hence the solution is x = -3, 3.**

Let us look at the next problem on "Integers and absolute value worksheet".

**Problem 3 :**

Solve the absolute value function |2x + 5| + 6 = 7

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k **

**|2x + 5| + 6 = 7 ------------> |2x+5| = 1**

When we apply the method explained above for |2x + 5| = 1,

we get 2x + 5 = 1 or 2x + 5 = -1

2x = -4 or 2x = -6

x = -2 or x = -3

**Hence the solution is x = -2, -3.**

Let us look at the next problem on "Integers and absolute value worksheet"

**Problem 4 :**

Solve the absolute value function |x - 3| + 6 = 6

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k **

**|x - 3| + 6 = 6 ------------> |x - 3| = 0**

When we apply the method explained above for |x - 3| = 0,

we get x -3 = 0 or x -3 = 0

x = 3 or x = 3

**Hence the solution is x = 3, 3.**

Let us look at the next problem on "Integers and absolute value worksheet"

**Problem 5 :**

Solve the absolute value function 2|3x +4| = 7

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k **

**2|3x+4| = 7 -------> |3x+4| = 7/2**

When we apply the method explained above for |3x + 4| = 7/2,

we get 3x + 4 = 7/2 or 3x + 4 =-7/2

3x = 7/2 - 4 or 3x = -7/2-4

3x = -1/2 or 3x = -15/2

x = -1/6 or x = -5/2

**Hence the solution is x = -1/6, -5/2**

Let us look at the next problem on "Integers and absolute value worksheet"

**Problem 6 :**

Solve the absolute value function 3|5x - 6|- 4 = 5

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k **

**3|5x-6|-4 = 5 -------> 3|5x-6| = 9 ------->|5x-6| = 3**

When we apply the method explained above for |5x - 6| = 3,

we get 5x - 6 = 3 or 5x -6 = -3

5x = 9 or 5x = 3

x = 9/5 or x = 3/5

**Hence the solution is x = 9/5, 3/5**

Now, let us look at a problem on "Integers and absolute value" with quadratic polynomial in absolute sign.

**Problem 7 :**

Solve the absolute value function |x² - 4x - 5| = 7

**Solution :**

When we apply the method explained above for |x²-4x-5| = 7,

we get x² - 4x - 5 = 7 or x² -4x - 5 = -7

x² - 4x - 12 = 0 or x² - 4x + 2 = 0

Here we have quadratic equations.

**Let us solve the first quadratic equation x² - 4x - 12 = 0**

x² - 4x - 12 = 0 ----------> (x+2)(x-6) = 0

x + 2 = 0 (or) x - 6 = 0

x = -2 (or) x = 6

**Let us solve the second quadratic equation x² - 4x + 2 = 0**

This quadratic equation can not be solved using factoring. Because the left side part can not be factored.

So, we can use quadratic formula and solve the equation as given below.

Let us look at the next problem on "Integers and absolute value worksheet"

**Problem 8 :**

Solve the absolute value function 0.5|0.5x| - 0.5 = 2.5

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k **

**0.5|0.5x****|-0.5=2.5 ------> 0.5|0.5x****|=3 ------> |0.5x| = 6**

When we apply the method explained above for |0.5x| = 6,

we get 0.5x = 6 or 0.5x = -6

x = 12 or x = -12

**Hence the solution is x = -12, 12**

Now let us look at some quiet different problems on "Integers and absolute value"

**Problem 9 :**

If the absolute value equation |2x+k| = 3 has the solution x= -2, find the value of "k".

**Solution :**

Since x = -2 is a solution, we can plug x = -3 in the given absolute value equation |2x+k| = 3.

|2(-2)+k| = 3 -------|-4+k| = 3

Using the method explained above, we get

-4 + k = 3 or -4 + k = -3

k = 7 or k = 1

**Hence, the value of k = 1, 7**

Let us look at the next problem on "Integers and absolute value worksheet"

**Problem 10 :**

If the absolute value equation |x - 3| - k = 0 has the solution x = -5, find the value of "k".

**Solution :**

Let us write the given absolute value equation in the form

**|x+a| = k**

**|x-3|-k --------> |x-3| = k**

Since x = 5 is a solution, we can plug x = 5 in the absolute value equation |x-3| = k

|-5-3| = k

|-8| = k

8 = k (absolute value of any negative number is positive)

**Hence the value of k = 8.**

**Please click here to download "Solving absolute value equations pdf"**

After having gone through the step by step solutions for all the problems on "Integers and absolute value worksheet", we hope that the students would have understood how to do problems on "Integers and absolute value worksheet".

If you want to know more about "Integers and absolute value worksheet", please click here.

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**