To solve the equation:

$\frac{5}{2} - 2g = \frac{5}{2}g - 3 + g$

Let's proceed step-by-step.

Step 1: Combine like terms on the right side

Rewrite $\frac{5}{2}g - 3 + g$ as a single term with $g$ and constants: $\frac{5}{2} - 2g = \frac{5}{2}g + g - 3$ Combine $\frac{5}{2}g$ and $g$ (which is equivalent to $1g$ or $\frac{2}{2}g$): $\frac{5}{2} - 2g = \frac{7}{2}g - 3$

Step 2: Move terms involving $g$ to one side and constants to the other side

Add $2g$ to both sides to move the $g$-terms together: $\frac{5}{2} = \frac{7}{2}g + 2g - 3$ Convert $2g$ to a fraction with denominator 2: $\frac{5}{2} = \frac{7}{2}g + \frac{4}{2}g - 3$ Combine terms on the right side: $\frac{5}{2} = \frac{11}{2}g - 3$

Step 3: Move the constant to the left side

Add 3 to both sides to isolate the $g$-term: $\frac{5}{2} + 3 = \frac{11}{2}g$ Convert 3 to a fraction with denominator 2: $\frac{5}{2} + \frac{6}{2} = \frac{11}{2}g$ Combine the fractions on the left: $\frac{11}{2} = \frac{11}{2}g$

Step 4: Solve for $g$

Since both sides are equal and have the same coefficient of $g$: $g = 1$

Final Answer

$g = 1$

Would you like further details on each step or have additional questions?

1. How do we handle fractions in equations involving variables?
2. Can you provide more examples of combining like terms in equations?
3. How would the solution change if we had a different constant term on the right side?
4. What are common mistakes to avoid when moving terms across the equals sign?
5. How do we verify if the solution is correct?

Tip: When solving equations, always check your solution by plugging it back into the original equation to confirm it satisfies all terms.