Question

Solve the equation. Graph and check your solutions. - 3|x| = - 15 Select the correct choice and, if necessary, fill in the answer box in your choice below. .

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

Answer 1

To solve the equation -3|x| = -15, we need to isolate the absolute value term.

First, we divide both sides of the equation by -3 to get rid of the coefficient:
|x| = 5

Now, we need to consider two cases for the absolute value: positive and negative.

Case 1: x is positive
If x is positive, then |x| is equal to x. So we have:
x = 5

Case 2: x is negative
If x is negative, then |x| is equal to -x. So we have:
-x = 5

To solve for x in this case, we need to multiply both sides by -1:
x = -5

Therefore, the solutions to the equation are x = 5 and x = -5.

To graph the equation, we plot the points (5,0) and (-5,0) on a number line. The graph would be:

----------------0-----|-----5-----|-----0-----|-----5-----|-----0----

Checking the solutions:
For x = 5:
-3|x| = -3(5) = -15
-15 = -15 (true)

For x = -5:
-3|x| = -3(-5) = -15
-15 = -15 (true)

Both solutions satisfy the original equation, so they are correct.