Question

How many solutions does the following equation have? \[-6(x 7)=-4x-2\] choose 1 answer: choose 1 answer: (choice a) no solutions a no solutions (choice b) exactly one solution b exactly one solution (choice c) infinitely many solutions c infinitely many solutions

Answer 1

The equation -6(x + 7) = -4x - 2 simplifies to x = -20, hence there is exactly one solution to the equation.

Step-by-step explanation:

When analyzing the equation -6(x + 7) = -4x - 2, we aim to determine how many solutions it has. To do this, we first distribute the -6 to both terms inside the parentheses, resulting in -6x - 42, and then we rewrite the equation as -6x - 42 = -4x - 2. Next, we simplify the equation by adding 6x to both sides and adding 42 to both sides, which leads us to 0 = 2x + 40. Finally, we solve for x by subtracting 40 from both sides and dividing by 2, resulting in x = -20.

There is exactly one solution to the equation, which is x = -20. Therefore, the correct choice is (b) exactly one solution.