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 equation -6(x + 5) + 3 = -2(x + 4) - 4x simplifies to -19 = -6x and has one solution.

Step-by-step explanation:

To solve the equation -6(x + 5) + 3 = -2(x + 4) - 4x, we first simplify each side of the equation by distributing and combining like terms. This gives us -6x - 30 + 3 = -2x - 8 - 4x. Continuing to simplify, we have -6x - 27 = -6x - 8. Rearranging the equation, we have -27 + 8 = -6x + 6x - 6x, which simplifies to -19 = -6x. Dividing both sides by -6, we find that x = 19/6.

Therefore, the equation has one solution.

Any input value for the variable x will generate a true equation, as when substituting x = 19/6 back into the original equation, both sides will be equal.