Question

What is the absolute value of \[\left| -38 \right|\]?

Answer 1

Hint: In this problem, we have to solve and find the value of the given problem. Here we are given an absolute value equation. We know that an absolute value equation will always be positive. We have to use the property of absolute value equations. We can first apply the rule if \[\left| x \right|=k\] then \[x=k\] or \[x=-k\]. We can then solve the resulting equations, and put the solution into the original equation to get the correct root.

Complete step by step answer:
We know that the given absolute equation to be solved is,
 \[\Rightarrow \left| -38 \right|\]……. (1)
We are given an absolute value equation. We know that an absolute value equation will always be positive. We have to use the property of absolute value equations.
We can first apply the rule if \[\left| x \right|=k\] then \[x=k\] or \[x=-k\].
In this problem, if \[\left| x \right|=\left| -38 \right|\] then \[x=38\] or \[x=-38\].
Then we can write the absolute value,
 \[\Rightarrow \left| -38 \right|=38\]
We can see that the absolute value should be only positive, i.e. the number inside the modulus (either with positive or negative sign) should be taken as positive.

Therefore, the absolute value of \[\left| -38 \right|=38\]

Note: Students make mistakes while following the steps to solve the absolute value equations. We should first apply the rule and solve for x. We should then substitute the value of x, to check whether the condition for the property of absolute value, i.e. the rule if \[\left| x \right|=k\] then \[x=k\] or \[x=-k\] is correct.