Equations with Absolute Values - Examples, Exercises and Solutions

The "absolute value" may seem complicated to us, but it is simply the distance between a given number and the figure $0$ .

What is absolute value?

An absolute value is denoted by ││ and expresses the distance from zero points.
The absolute value of a positive number - will always be the number itself.
For example: $│2│= 2$
Absolute value of a negative number: will always be the same number, but positive.
For example: $│-3│=3$
Note that the absolute value of a number will always be a positive number since distance is always positive.

The absolute value of a number is the distance between it and the number 0.

For example:

The distance between the number $+7$ and $0$ is $7$ units. Therefore, the absolute value of $+7$ is $7$ .
The distance between the number $-7$ and $0$ is also $7$ units. Therefore, the absolute value of $-7$ will also be $7$ .

As we can see, from the point of view of absolute value, it doesn't matter if the number is positive or negative.

To denote the absolute value, the number is written between two vertical lines.

Practice Equations with Absolute Values

Question 1

$\left|18\right|=$

Question 2

$\left|-2\right|=$

Question 3

$\left|3\right|=$

Question 4

$\left|0.8\right|=$

Question 5

$\left|x\right|=5$

Examples with solutions for Equations with Absolute Values

Exercise #1

$\left|18\right|=$

Video Solution

Video Solution

Answer

Answers a + b

Question 1

$\left|x-1\right|=6$

Question 2

$\left|6x-12\right|=6$

Question 3

$\left|x-10\right|=0$

Question 4

$\left|x+1\right|=5$

Answer

$x$

Question 1

$\left|3^2\right|=$

Question 2

$\left|-19\frac{1}{4}\right|=$

Question 3

$−\left|-18\right|=$

Question 4

$-\lvert4^2\rvert=$

Answer

$x=-10$ , $x=10$

Topics learned in later sections