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.
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.
To solve the equation -3|x| = -15, we can start by isolating the absolute value term.
First, divide both sides of the equation by -3 to get rid of the coefficient:
|x| = 5
Now, we know that the absolute value of x is equal to 5. This means that x can be either positive or negative 5.
To graph the solution, we can plot two points: (5, 0) and (-5, 0). These points represent the two possible solutions for x.
Checking the solutions:
When x = 5:
-3(5) = -15
-15 = -15 (True)
When x = -5:
-3(-5) = -15
15 = -15 (False)
Therefore, the only solution is x = 5.
So, the correct choice is:
A. x = 5
To solve the equation -3|x| = -15, we can start by isolating the absolute value term.
First, divide both sides of the equation by -3:
|x| = (-15) / (-3)
Simplifying gives:
|x| = 5
Now, we need to consider both the positive and negative values that could satisfy the absolute value equation.
For x to be positive, the equation becomes:
x = 5
And for x to be negative, the equation becomes:
-x = 5
Solving the second equation for x by multiplying both sides by -1 gives:
x = -5
So the possible solutions are x = 5 and x = -5.
To graph and check the solutions, plot the points (5, 0) and (-5, 0) on the number line. Then, substitute these values back into the original equation:
-3|5| = -15
-3(5) = -15
-15 = -15
The equation is satisfied when x = 5.
Next, substitute x = -5 back into the equation:
-3|-5| = -15
-3(5) = -15
-15 = -15
The equation is also satisfied when x = -5.
Therefore, the correct choice is:
x = 5, -5