Question

Solve 3|3x+4| =12
a. x = 2
b. x = -2
c. x = -4
d. x = 4

Answer 1

To solve the equation 3|3x+4| = 12, divide both sides by 3, consider two cases, and solve for x to find the solutions.

Step-by-step explanation:

To solve the equation 3|3x+4| = 12, we need to isolate the absolute value expression on one side of the equation. We can do this by dividing both sides of the equation by 3. This gives us |3x+4| = 4.

Now we need to consider two cases:

1. If 3x+4 is positive or zero, then |3x+4| is equal to 3x+4. In this case, we can write the equation as 3x+4 = 4. Solving for x, we get x = 0.
2. If 3x+4 is negative, then |3x+4| is equal to -(3x+4). In this case, we can write the equation as -(3x+4) = 4. Solving for x, we get x = -2.

Therefore, the solutions to the equation 3|3x+4| = 12 are x = 0 and x = -2.