Question

How do you solve the given equation $\left| x-10 \right|=3$?

Answer 1

We start solving the problem by recalling the fact that the solution of the given equation $\left| x \right|=a$, for $a\ge 0$ as $x=\pm a$. We then compare whether the R.H.S (Right Hand Side) of the given equation satisfies the condition $a\ge 0$ to proceed through the problem. We then apply the fact $x=\pm a$ and then make the necessary calculations to get the required solution (the values of x) of the given equation.

Complete step by step answer:
According to the problem, we are asked to solve the given equation $\left| x-10 \right|=3$.
We have given the equation $\left| x-10 \right|=3$ ---(1).
We know that the solution of the given equation $\left| x \right|=a$, for $a\ge 0$ is defined as $x=\pm a$. Let us use this result in equation (1).
We can see that 3 satisfies the given condition $a\ge 0$ to proceed through the problem.
So, we have $x-10=\pm 3$.
Let us assume $x-10=3$.
So, we get $x=10+3=13$.
Now, let us assume $x-10=-3$.
So, we get $x=10-3=7$.
So, we have found the solution(s) of the given equation $\left| x-10 \right|=3$ as $x=13$, 7.
$\therefore$ The solution(s) of the given equation $\left| x-10 \right|=3$ is $x=13$, 7.

Note: Whenever we get this type of problem, we first check whether the given number in the R.H.S (Right Hand Side) satisfies the condition $a\ge 0$. We should not make the calculation mistakes while solving these types of problems. We should consider both the positive and negative values on the R.H.S (Right Hand Side) to get the required solution. Similarly, we can expect problems to find the solution of the given equation $\left| x-3 \right|=-2$.