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To solve the given equation, isolate z to one side of the equal sign, this way:
1. Substract 2 to both sides of the equation:
[tex]\begin{gathered} 6z+3-2=2-2 \\ 6z+1=0 \end{gathered}[/tex]2. Substract 1 to both sides of the equation:
[tex]\begin{gathered} 6z+1-1=0-1 \\ 6z=-1 \end{gathered}[/tex]3. Divide both sides of the equation by 6:
[tex]\begin{gathered} \frac{6}{6}z=-\frac{1}{6} \\ z=-\frac{1}{6} \end{gathered}[/tex]z has a value of -1/6.