Question

Examine the solution to the equation. –6(x + 5) + 3 = –2(x + 4) – 4x –6x – 30 + 3 = –2x – 8 – 4x –6x – 27 = –6x – 8 –27 = – 8 Which statements accurately describe this equation? Check all that apply.

This equation has one solution.
This equation has no solution.
This equation has infinitely many solutions.
Any input value for the variable will generate a true equation.
Any input value for the variable will generate a false equation.

Answer 1

The correct answers are B and E

your welcome!

Answer 2

option (2) and (5) is correct.

2) This equation has no solution.

5) Any input value for the variable will generate a false equation.

Explanation:

Given a solution to the equation,

-6( x + 5) + 3 = -2( x + 4) - 4x

⇒ –6x – 30 + 3 = –2x – 8 – 4x

⇒ –6x – 27 = –6x – 8

⇒ –27 = – 8

Which is false statement as -27 is never equal to -8.

Thus, This equation has no solution.

Also, if we substitute any value of x , then also the equality never hold.

For example lets put x = 1 in -6( x + 5) + 3 = -2( x + 4) - 4x , we get,

⇒ -6( 1 + 5) + 3 = -2( 1 + 4) - 4(1)

⇒ -6( 6) + 3 = -2(5) - 4

⇒ -36 + 3 = -10 - 4

⇒ -33 = -14

Still the value is false as -33 is never equal to -14.

Any input value for the variable will generate a false equation.

Thus, option (2) and (5) is correct.