Question

If | 3x – 2 | + x = 11, then x =
(a) $\dfrac{13}{4}$
(b) \[-\dfrac{9}{2}\]
(c) $\dfrac{5}{7}$
(d) $-\dfrac{6}{7}$

Answer 1

Hint: Here, we will just follow the basic principle of modulus along with some basic mathematical operations such as subtraction and addition to find the required result.

Complete step-by-step answer:
We have here, | 3x – 2 | + x = 11
Here the expression in the modulus can give us either negative or positive value.
Therefore,
$\pm $(3x – 2) + x = 11
Now, let us find the value of x for both the conditions.
When, (3x – 2) + x = 11
              3x – 2 + x = 11
              4x – 2 = 11
Let us add 2 on both the sides of the equation, we get
4x – 2 + 2 = 11 + 2
4x = 13
  x = $\dfrac{13}{4}$
Now, let us check for the other condition.
When, – (3x – 2) + x = 11
Let us multiply by – 1 so that we can open the bracket and solve further, we get

– 3x + 2 + x = 11
– 2x + 2 = 11
Now, let us subtract by 2 on both the sides of the equation, we get
– 2x + 2 – 2 = 11 – 2
– 2x = 9
x = $-\dfrac{9}{2}$
But we know, when | x | = x if x is greater than equal to 0.
Hence, the value of x is equal to $\dfrac{13}{4}$.

So, the correct answer is “Option A”.

Note: The modulus of a positive expression is positive, but if there was a negative expression inside the modulus, it would have been turned to positive due to the modulus. Also, find all the possible values to determine the correct answer which is present in the multiple choices.