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Solve for zz.\newline0=3z0 = |-3z|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinez=z = _____ or z=z = _____

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Q. Solve for zz.\newline0=3z0 = |-3z|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinez=z = _____ or z=z = _____
  1. Understand absolute value equation: Understand the absolute value equation.\newlineThe equation given is 0=-3z0 = |\text{-}3z|. The absolute value of any number is always non-negative. Therefore, the only way for the absolute value of something to equal 00 is for the inside of the absolute value to be 00.
  2. Set inside equal to 00: Set the inside of the absolute value equal to 00.\newlineSince 3z=0|-3z| = 0, we can remove the absolute value bars and set the inside equal to 00.\newline3z=0-3z = 0
  3. Solve for z: Solve for z.\newlineDivide both sides of the equation by 3-3 to isolate zz.\newlinez=0/3z = 0 / -3\newlinez=0z = 0
  4. Check for second solution: Check for a second solution.\newlineNormally, an absolute value equation x=a|x| = a has two solutions, x=ax = a and x=ax = -a. However, since 00 is the only number that is its own negative, there is only one solution in this case.\newlinez=0z = 0

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