(1) $$ \frac{3 z-1}{3}-\frac{x+3}{2} $$

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UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (3z-1)/3-(x+3)/2 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(3z-1ight)}{3}-\frac{\left(x+3ight)}{2}$$
- step1: Remove the parentheses:
  $$\frac{3z-1}{3}-\frac{x+3}{2}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{\left(3z-1ight)	imes 2}{3	imes 2}-\frac{\left(x+3ight)	imes 3}{2	imes 3}$$
- step3: Multiply the numbers:
  $$\frac{\left(3z-1ight)	imes 2}{6}-\frac{\left(x+3ight)	imes 3}{2	imes 3}$$
- step4: Multiply the numbers:
  $$\frac{\left(3z-1ight)	imes 2}{6}-\frac{\left(x+3ight)	imes 3}{6}$$
- step5: Transform the expression:
  $$\frac{\left(3z-1ight)	imes 2-\left(x+3ight)	imes 3}{6}$$
- step6: Multiply the terms:
  $$\frac{6z-2-\left(x+3ight)	imes 3}{6}$$
- step7: Multiply the terms:
  $$\frac{6z-2-\left(3x+9ight)}{6}$$
- step8: Subtract the terms:
  $$\frac{6z-11-3x}{6}$$
The simplified form of the expression $$ \frac{3z-1}{3}-\frac{x+3}{2} $$ is $$ \frac{6z-11-3x}{6} $$.
The simplified form of the expression is $$ \frac{6z - 11 - 3x}{6} $$.

(1) \( \frac{3 z-1}{3}-\frac{x+3}{2} \)

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