Question

Solve the expression: $\left| {3x - 5} \right| = 1$

Answer 1

We have to find the value of $x$ from the given expression $\left| {3x - 5} \right| = 1$ . We solve this question using the concept of solving linear equations and the concept of splitting of modulus functions . First we would simplify the terms of the left hand side by splitting the modulus function and taking plus - minus on one side i.e. either on the left hand side or on the right hand side , we would obtain two relations in terms of $x$ . On further solving the two expressions we get the values of $x$ .

Complete step-by-step solution:
Given :
$\left| {3x - 5} \right| = 1$
Splitting the modulus function , we get
$\left( {3x - 5} \right) = \pm 1$
Let us consider the expression as two cases as :
$Case{\text{ }}1{\text{ }}:$
$3x - 5 = 1$
Simplifying the terms , we get
$3x = 1 + 5$
$3x = 6$
Cancelling the terms , we get the value of $x$ as :
$x = 2$
$Case{\text{ }}2{\text{ }}:$
$3x - 5 = - 1$
Simplifying the terms , we get
$3x = - 1 + 5$
$3x = 4$
Solving the term , we get the value of $x$ as :
$x = \dfrac{4}{3}$
Hence, the value of $x$ for the given expression $\left| {3x - 5} \right| = 1$ are $2$ and $\dfrac{4}{3}$.

Note: Modulus function: It is a function which always gives a positive value when applied to a function irrespective of the values of the function . The graph of a modulus function is a V shaped graph where the tip is the point of contact on the graph . We add $\pm$ for removing the modulus function as we don’t know the value was taken as negative or positive , so to remove errors while solving we add $\pm$ sign and solve it for two cases separately .
Example : The value of a mod function is as given below
$\left| { - 1} \right| = 1$
$\left| 1 \right| = 1$
We get the value as $1$ for both $+ 1$ or $- 1$ .