Question

How much less than $3{{a}^{2}}-6$ is $2{{a}^{2}}+1$? State True or False: the answer is ${{a}^{2}}-7$.
A) True
B) False

Answer 1

Hint: By taking subtraction of two equations we might find the answer. And then after finding the answer we have to prove whether it is true or false compared to that given in the question.
Complete step-by-step answer:
Here, we are given two equations which are:
$3{{a}^{2}}-6$ ………………(i)
$2{{a}^{2}}+1$ ………………(ii)
Here, it is like $x-?=b$ as it is told how much less means we have to do subtraction and find ? sign value.
Using the above concept to find how much is equation (i) less than equation (ii), we have to subtract equation (ii) from (i) i.e.
$\left( 3{{a}^{2}}-6 \right)-?=\left( 2{{a}^{2}}+1 \right)$
$\Rightarrow 3{{a}^{2}}-6-\left( 2{{a}^{2}}+1 \right)=?$
$\Rightarrow 3{{a}^{2}}-6-2{{a}^{2}}-1=?$
$\Rightarrow {{a}^{2}}-7=?$
Hence, the solution of the question is ${{a}^{2}}-7$.
Now, in question the given answer is ${{a}^{2}}-7$ which is similar to our answer. Hence, we can say that answer is True.
So, the correct option is (A).

Note: In such type of question students might make mistake by subtracting equation (i) from equation (ii) which becomes $2{{a}^{2}}+1-\left( 3{{a}^{2}}-6 \right)$, which is opposite to our solution and due to that answer also becomes $2{{a}^{2}}+1-3{{a}^{2}}+6\Rightarrow \left( -{{a}^{2}}+7 \right)$ which is False and thus the whole problem goes wrong. So, students must take care while understanding the terminology and solve accordingly.