Questions: 3(4g+6)=2(6g+9)

Transcript text: $3(4 g+6)=2(6 g+9)$

Solution

Solution Steps

To solve the equation $3(4g + 6) = 2(6g + 9)$, we will first expand both sides of the equation. Then, we will collect like terms and solve for the variable $g$.

Step 1: Expand Both Sides

First, we expand both sides of the equation: \[ 3(4g + 6) = 2(6g + 9) \]

Expanding gives: \[ 12g + 18 = 12g + 18 \]

Step 2: Simplify the Equation

After expanding, we notice that both sides of the equation are identical: \[ 12g + 18 = 12g + 18 \]

Step 3: Analyze the Equation

Since both sides of the equation are identical, this implies that the equation is true for all values of $ g $. Therefore, there are infinitely many solutions.

Final Answer

The solution to the equation is that $ g $ can be any real number. Thus, the solution is: \[ \boxed{\text{All real numbers}} \]

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