Final answer:
To solve the equation -10 2/3 |x| = -4, we first isolate the absolute value of x by dividing both sides by -10 2/3, leading to the solutions x = 3/8 or x = -3/8.
Step-by-step explanation:
The equation given is -10 2/3 |x| = -4. To solve for x, we first need to isolate the absolute value of x. We start by dividing both sides of the equation by -10 2/3 to get |x| on one side.
First, convert -10 2/3 to an improper fraction: -10 2/3 = -32/3. Now divide -4 by -32/3:
|x| = -4 / (-32/3) = 4 / (32/3) = 3/8
Since the absolute value of x equals 3/8, x can be either 3/8 or -3/8. Therefore, the solution to the equation is x = 3/8 or x = -3/8.