Question

Determine which equation below has a solution of a = 2.
A. 2a + 3a – 6 = –21
B. 8 = 3 + 4a – 3 – 5a
C. –2 = 2 + 5a – 2 – 6a
D. –4a + 3a – 6 = –4

Answer 1

Insert a = 2 in each equation and check , if you get 0 = 0, then that is the answer.

Answer 2

Or solve each equation by solving for a.

Example :

A. 2a + 3a - 6= -21

\(\color{blue}{2a + 3a } = 5a\)
Therefore : \(\color{blue}{2a + 3a} - 6 = -21 \\
\implies \color{blue}{5a } - 6= -21\)

Add 6 both sides.

\(5a \color{red}{-6} + \color{red}{6} = -21 + \color{red}{6}\)

Notive : - 6 + 6 there. -6 + 6 = 0

Therefore: \(5a = -21 + 6\)

\(5a = -15\)

Divide both sides by 5

\(\cfrac{5a}{5} = \cfrac{-15}{5}\)
\(a = -3\)

But, we have to find that equation which has soln of a = 2 , but here a= -3 . Therefore A.) can not be out correct choice.

Similarly do for all.

Answer 3

You can also do that by inserting a =2 in each equation...

Example : A.) 2a + 3a - 6 = -21

2(2) + 3(2) - 6 = -21

4 + 6 - 6 = -21

4 +0 = -21

4 = -21

By putting a = 2 in the equation, we get 4 = -21 which is not true.

Therefore, a = 2 is not the solution of this equation. i.e. A.) is not our correct choice.