How many solutions does the following equation have?

|4x + 12| = 0

one solution

recall that the definition of |x| is
|x| = x if x >= 0
|x| = -x if x < 0

so, |4x+12| = 4x+12
if 4x+12 = 0

−6(x+7)=−4x−2

How many solutions does the following equation have?

vrewg

To determine the number of solutions for the equation |4x + 12| = 0, we need to consider the absolute value property.

The absolute value of a number is always non-negative, meaning it is either zero or positive.

Therefore, for the equation |4x + 12| = 0, the only way for the absolute value to be equal to zero is if the expression inside the absolute value bars, 4x + 12, is equal to zero.

So we can solve the equation 4x + 12 = 0 to find the solution(s):

4x + 12 = 0

Subtracting 12 from both sides:

4x = -12

Dividing both sides by 4:

x = -12/4

Simplifying, we get:

x = -3

Therefore, the equation |4x + 12| = 0 has one solution, x = -3.