Examples of Absolute Value
Example 1: Solve 3 | x – 2 | = 15
Solution:
Given,
- 3| x – 2 | = 15
| x – 2 | = 5
x – 2 = 5 or x – 2 = -5
x = 7 or x = -5 + 2 = -3
Example 2: Solve | 2x2 – 1 | = | x2 + 2 |
Solution:
Given,
- | 2x2 – 1 | = | x2 + 2 |
Using Property, | x | = | y | ⇒ x = ± y
2x2 – 1 = x2 + 2 and 2x2 – 1 = – ( x2 +2 )
⇒ x2 = 3 and 2x2 -1 = -x2 -2
⇒ x = ±√ 3 and 3x2 = -1
⇒ x = ±√ 3 and x = ±√( -1 / 3 ) = ± i / √ 3 = ± √( 3 ) i/3
⇒ x = ±√ 3 and x = ± (√3) i/3
Example 3: What is the value of 5 | 7x – 1 | if x = – 2 ?
Solution:
Given,
- Find the value of, 5| 7x – 1 | if, x = – 2
= 5 | 7(-2) – 1 |
= 5 | -14 -1 |
= 5 | -15 |
= 5 ( 15 )
= 75
Value of 5 | 7x – 1 | = 75, when x = -2
Absolute Value
Absolute Value for a number x is denoted by |x|, pronounced as “module x”. It is also referred to as numbers or magnitudes. Absolute values are only numeric values and do not include the sign of the numeric value.
Let’s learn about Absolute value in detail, including its symbol, properties, graph, and examples.
Table of Content
- What is Absolute Value?
- Absolute Values of a Number
- Absolute Value of 0
- Absolute Value Function
- Absolute Value Function Graphs
- Absolute Value of Complex Number
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