Question

What should be subtracted from 2a + 6b – 5 to get ─3a + 2b + 3?
(a) 5 + 4b – 8
(b) 5a + 4b – 8
(c) 5a + 4ab – 8
(d) 5a + 4b – 10

Answer 1

Hint: To solve this question, we will consider a variable for the required expression. It is given that if the required expression is subtracted from 2a + 6b – 5, we get ─3a + 2b + 3. Thus, if ─3a + 2b + 3 is subtracted from 2a + 6b – 5, we shall get the required expression. An example of this concept is if 2 is subtracted from 7 to get 5, if we subtract 5 from 7, we will get 2. Going on similar lines, we will get the required expression.

Complete step by step answer:
Let x be the expression which when subtracted from 2a + 6b – 5 yields ─3a + 2b + 3.
$\Rightarrow $ 2a + 6b – 5 – x = ─3a + 2b + 3
Thus, if ─3a + 2b + 3 is subtracted from 2a + 6b – 5, we shall get the required expression x.
$\Rightarrow $ x = 2a + 6b – 5 – (─3a + 2b + 3)
First of all, we shall solve the parenthesis. To do that we shall multiply ─3a + 2b + 3 by negative sign.
$\Rightarrow $ x = 2a + 6b – 5 + 3a – 2b – 3
Now, we will bring the terms with the same variable together.
$\Rightarrow $ x = 2a + 3a + 6b – 2b – 5 – 3
Further, we shall take the variables as common.
$\Rightarrow $ x = (2 + 3)a + (6 – 2)b – (5 + 3)
Now, we will perform the arithmetic operations on numerical values.
$\Rightarrow $ x = 5a + 4b – 8
Thus, we have to subtract 5a + 4b – 8 from 2a + 6b – 5 to get ─3a + 2b + 3.

So, the correct answer is “Option B”.

Note: Students are advised to verify the answer they got for the given conditions. To verify, we will subtract 5a + 4b – 8 from 2a + 6b – 5. Thus, 2a + 6b – 5 – (5a + 4b – 8). We will take variables common and execute the operation inside the parenthesis. a(2 – 5) + b(6 – 4) – 5 + 8. After subtraction, we get ─3a + 2b + 3.