Question

Verify that \[ - \left( { - x} \right) = x\] for \[x = \dfrac{{10}}{{13}}\]

Answer 1

Hint: Given is a value of a variable such that the variable is a fraction. This fraction is positive. Now we will check whether this value holds for the given condition or not. For that we will put this value so given in place of x and then apply the laws of algebra.

Complete step by step answer:
Given that, \[x = \dfrac{{10}}{{13}}\].
Now \[ - x = - \dfrac{{10}}{{13}}\] that is nothing but the fraction becomes a negative number now. But according to the condition we have to multiply it one more time by a negative sign.
\[ - \left( { - x} \right) = - \left( { - \dfrac{{10}}{{13}}} \right)\]
Now as we know, the product of two minus signs is always a plus sign. So the value becomes,
\[ - \left( { - x} \right) = \dfrac{{10}}{{13}}\]
And coincidentally this is the original value of x that is ,
\[ - \left( { - x} \right) = \dfrac{{10}}{{13}} = x\]

So the given value of x holds or we can say is verified for the given condition.

Note: Here note that, the rules of signs for addition and multiplication are different.
Also if the given number is itself negative like say \[x = - \dfrac{{10}}{{13}}\] then probably the condition may be different.
\[ - \left( { - x} \right) = - \left( { - \left( { - \dfrac{{10}}{{13}}} \right)} \right)\]
Now when three minus signs are multiplied we get a minus sign only.
\[ - \left( { - x} \right) = - \dfrac{{10}}{{13}}\]
Thus it holds for negative values also.