Solve.
vertical bar z minus 8 vertical bar equals 4
A. z equals negative 4, z = 4 ***
B. z equals negative 12, z = 12
C. z equals negative 12, z equals negative 4
D. z = 4, z = 12
im confused, can someone explain it to me please?
|z-8| = 4.
z - 8 = (+-)4,
z = (+-)4 + 8 = 12, and 4. D.
To solve the equation |z - 8| = 4, we can use the definition of absolute value. The absolute value of a number is its distance from zero on the number line.
We have two possibilities for the expression inside the absolute value: (z - 8) and -(z - 8). Let's solve for both cases:
1. z - 8 = 4:
Add 8 to both sides to isolate z:
z = 4 + 8 = 12
2. -(z - 8) = 4:
Multiply both sides by -1 to get rid of the negative sign:
z - 8 = -4
Add 8 to both sides:
z = -4 + 8 = 4
So we have two potential solutions: z = 12 and z = 4. Therefore, the correct answer is D. z = 4, z = 12.