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.