Q. Solve for z.0=∣4z∣Write your answers as integers or as proper or improper fractions in simplest form.z= _____ or z= _____
Understand absolute value equation: Understand the absolute value equation.The equation given is 0=∣4z∣. The absolute value of any number is always non-negative. Therefore, if the absolute value of something is equal to 0, the only possibility is that the expression inside the absolute value is itself 0.
Set inside equal to 0: Set the inside of the absolute value equal to 0.Since ∣4z∣=0, we can conclude that 4z must be equal to 0 because that is the only value whose absolute value is 0.
Solve for z: Solve for z.To find z, we divide both sides of the equation 4z=0 by 4.z=0/4z=0
Check for second solution: Check for a second solution.Normally, with absolute value equations, we would check for a second solution by considering the negative of the inside expression. However, since 0 is the only number that is equal to its own negative, there is no second solution in this case.