Q. Solve for z.0=∣−3z∣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=∣-3z∣. The absolute value of any number is always non-negative. Therefore, the only way for the absolute value of something to equal 0 is for the inside of the absolute value to be 0.
Set inside equal to 0: Set the inside of the absolute value equal to 0.Since ∣−3z∣=0, we can remove the absolute value bars and set the inside equal to 0.−3z=0
Solve for z: Solve for z.Divide both sides of the equation by −3 to isolate z.z=0/−3z=0
Check for second solution: Check for a second solution.Normally, an absolute value equation ∣x∣=a has two solutions, x=a and x=−a. However, since 0 is the only number that is its own negative, there is only one solution in this case.z=0