Final answer:
To rewrite the given expression in the form [z], add fractions with a common denominator to isolate z on one side of the equation. The expression can be rewritten as z = 38/15.
Step-by-step explanation:
To rewrite the expression in the form [z], we need to isolate z on one side of the equation. Let's start with the given equation:
left(z - \frac{4}{3}) - \frac{6}{5} = 0
We can begin by adding \frac{6}{5} to both sides of the equation to eliminate the negative fraction:
z - \frac{4}{3} = \frac{6}{5}
Next, we can add \frac{4}{3} to both sides of the equation to isolate z:
z = \frac{4}{3} + \frac{6}{5}
To add the fractions, we need a common denominator. Both fractions already have the denominator of 3 and 5, so we can add the numerators directly:
z = \frac{4}{3} + \frac{6}{5} = \frac{20}{15} + \frac{18}{15} = \frac{38}{15}
Therefore, the expression in the form [z] is z = \frac{38}{15}.