Solve the equation. Graph and check your solutions. - 4|x| = - 20 Select the correct choice and, if necessary, fill in the answer box in your choice below.

OA. x = (Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution.

1 answer

To solve the equation - 4|x| = - 20, we will begin by isolating the absolute value expression.

Dividing both sides of the equation by -4, we get:

|x| = 5

Next, we can split the absolute value equation into two separate equations, one positive and one negative.

For the positive case:
x = 5

For the negative case:
-x = 5
Multiplying by -1 on both sides of the equation, we get:
x = -5

So we have two solutions: x = 5 and x = -5.

To graph these solutions, we can plot the two points (5, 0) and (-5, 0) on a number line.

Checking the solutions back into the original equation:

For x = 5:
-4(5) = -20
-20 = -20 (True)

For x = -5:
-4(-5) = -20
20 = -20 (False)

The only solution that satisfies the original equation is x = 5.

Therefore, the correct choice is:
OA. x = 5