Question

How do you solve \[\left| {3x - 5} \right| = - 2\]?

Answer 1

Hint:The above given equation is an example of absolute value equation.
Absolute value equations: Absolute value equations are the equations where the variable is within an absolute value operator, also known as a modulus operator. So while considering an absolute value equation involving variables we have to consider both the cases of positive and negative signs.

Complete step by step solution:
Given
\[\left| {3x - 5} \right| = - 2...........................\left( i \right)\]
Now in order to solve the given equation we need to solve for$x$.
Such that we have to manipulate the given equation in terms of only$x$, which can be achieved by performing different arithmetic operations on both LHS and RHS equally.
But here if we observe the equation we can see that the RHS is a negative number such that the absolute value of $3x - 5$ equals to a negative number.
Now we know the basic rule that an absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
So applying the basic rule in this question we can conclude that there would be no solution for \[\left| {3x - 5} \right| = - 2\] since an absolute value cannot be negative.

Note: Now before attempting a question involving absolute values one must check whether it’s equated to a positive or a negative number and then proceed accordingly. Also if we get a solution it can be checked whether it’s right or wrong by substituting the value of the variable back into the equation and checking whether it satisfies the given equation or not.