Question

For the equations given below, which statement is true? -3x - 8 = 19 and -3x - 2 = 25 A. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation. B. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation. C. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation. D. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

Answer 1

Answer:

Option (B) is correct.

Step-by-step explanation:

Given equations are:

- 3x - 8 = 19

Let the above be equation (i)

On solving, we have,

- 3x = 19 + 8

=> - 3x = 27

=> x = - 9

and - 3x - 2 = 25

Let this be equation (ii)

On solving, we get,

- 3x = 25 + 2

=> - 3x = 27

=> x = - 9

As both the equations have the same solution, we discard option(D)

Now, checking for the true statement from option (A) , (B) and (C)

According to option (A),

=>  - 3x - 8 - 6 = 19 - 6

=> - 3x - 14 = 13 ≠ - 3x - 2 = 25

=> - 3x - 14 = 13 ≠ the second equation

Therefore, option (A) is incorrect.

According to option (B),

=>  - 3x - 8 + 6 = 19 + 6

=> - 3x - 2 = 25 = - 3x - 2 = 25

=> - 3x - 14 = 13 = the second equation

Therefore, option (B) is correct.