Question

How do you solve\[\left| 3x \right|=9\] ?

Answer 1

Hint:In the given question, we have been asked to solve \[\left| 3x \right|=9\]. In order to solve this question, first we need to eliminate the absolute value sign.The number in the absolute value can either be positive or it can be negative also. You have to create two equations to eliminate the absolute value sign. We will make one equation that will give us a positive answer and another equation that will give us the negative answer.

Formula used:
\[\left| x \right|=\left\{ \dfrac{x\ if\ x\ge 0}{-x\ if\ x<0} \right.\]

Complete step by step answer:
We have the given equation:
\[\left| 3x \right|=9\]
Eliminate the absolute value sign, we need to create two equation, we get
\[3x=\pm 9\]
Two equation would be,
\[3x=9\] and \[3x=-9\]
Solving both the equations for the value of\[x\], we get
\[x=\dfrac{9}{3}=3\] and \[x=\dfrac{-9}{3}=-3\]

Therefore, the two values of \[x\] are 3, -3.

Note: In mathematics, the absolute value also called modulus of a real number \[x\], represent as \[\left| x \right|\]. Absolute value tells us about the distance from the number 0 on a number line irrespective of direction i.e. positive or negative. The absolute value of any number can never be negative, it is always positive because absolute value is the distance from the zero, so it will always remain positive. For example:- if you are -4 point , you can’t be -4 away from 0 as distance will never be negative. Therefore you are 4 points away from 0. If there are two or more than two operations will be present inside the absolute bars, you need to simplify that first and after that you will get absolute value.