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 inp/ value for the variable will generate a true equation Any input value for the variable will generate a false equation.
Mathematics · Middle School · Thu Feb 04 2021
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Given the equation:
-6(x + 5) + 3 = -2(x + 4) - 4x
Determine the solution of the equation.
Solution:
In order to determine the number of solutions, we first multiply -6 and -2 to each value inside their corresponding parenthesis. Then, we combine similar terms.
-6(x + 5) + 3 = -2(x + 4) - 4x
-6x - 30 + 3 = -2x + 6 - 4x
-6x - 27 = -6x + 6
Transpose -6x and 6 to the opposite sides of the equation, hence we must take note that in transposing a number, the sign changes.
-6x + 6x = -27 - 6
0 = -33
This means that we have no solution, since the value of x cancels out.
Final answer:
No Solution