Question

What is the value of x in modulus equation $\left| {x - 1} \right| = 5$ ?

Answer 1

Hint: This question is based on modulus, when we solve the modulus, we will get two values of x like in the equation. Solving the given modulus is similar to solving equations in that we do the majority of the same things, but we must pay attention to what is the property of the modulus.

Complete answer:
The modulus function is a function that returns the positive value of any variable or integer in general. The absolute value function, sometimes known as the absolute value function, may provide a non-negative value for any independent variable, whether positive or negative.
We can represent it as: $ \Rightarrow \left| {x - 1} \right| = 5$
Where x is the real number and y represents all positive numbers including 0.
We will see the properties of modulus:
If \[\left| x \right| = a{\text{ }}\]and a is greater than 0, then \[{\text{x = }} \pm a\] (1)
If \[\left| x \right| = a{\text{ }}\] and a is equal to zero, then \[{\text{x = 0}}\] (2)
If \[\left| x \right| = a{\text{ }}\]and a is less than zero, so there is no solution. (3)
We will solve $\left| {x - 1} \right| = 5$
$ \Rightarrow \left| {x - 1} \right| = 5$
We have a greater than zero. So, we will use the property 1
$ \Rightarrow x + 1 = \pm 5$
$ \Rightarrow x = 5 + 1 = 6$
$ \Rightarrow x = - 5 + 1 = - 4$
Hence, the value of x in $\left| {x - 1} \right| = 5$ are 6 and -4.

Note: The difficult type of question of modulus will also include inequality. Some properties are: The sign of an inequality is unaffected by adding or subtracting the same number from both sides of an inequation. Both sides of an inequation can be multiplied or divided by the same positive real number without changing the sign of the inequality, but when both sides of an inequation are multiplied or divided by a negative number, the sign of the inequality is reversed. Any term in an inequation can be transferred to the other side with its sign changed without changing the sign of the inequality.