Equation with absolute value - 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 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│2│= 2
Absolute value of a negative number: will always be the same number, but positive.
For example: 3=3│-3│=3
Note that the absolute value of a number will always be a positive number since distance is always positive.

Un valor absoluto se denota por ││

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

For example:

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

Exercise #1

18= \left|18\right|=

Video Solution

Answer

18 18

Exercise #2

0.8= \left|0.8\right|=

Video Solution

Answer

0.8 0.8

Exercise #3

3= \left|3\right|=

Video Solution

Answer

3 3

Exercise #4

2= \left|-2\right|=

Video Solution

Answer

2 2

Exercise #5

42= -\lvert4^2\rvert=

Video Solution

Answer

16 -16

Exercise #1

18= −\left|-18\right|=

Video Solution

Answer

18 -18

Exercise #2

1914= \left|-19\frac{1}{4}\right|=

Video Solution

Answer

1914 19\frac{1}{4}

Exercise #3

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

Video Solution

Answer

9 9

Exercise #4

x= \left|x\right|=

Video Solution

Answer

x x

Exercise #5

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

Video Solution

Answer

Answers a + b

Exercise #1

x10=0 \left|x-10\right|=0

Video Solution

Answer

x=10 x=10

Exercise #2

6x12=6 \left|6x-12\right|=6

Video Solution

Answer

x=1 x=1 , x=3 x=3

Exercise #3

x1=6 \left|x-1\right|=6

Video Solution

Answer

x=5 x=-5 , x=7 x=7

Exercise #4

x=5 \left|x\right|=5

Video Solution

Answer

Answers a + b

Exercise #5

y2= -\left|-y^2\right|=

Video Solution

Answer

y2 -y^2

Topics learned in later sections

  1. Absolute Value Inequalities
  2. Inequalities with Absolute Value