Question

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

Answer 1

Hint: 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 \[ - 1\] .