Problem

$\frac{5 x+9}{2}=12$

Answer

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Answer

Final Answer: \(\boxed{3}\)

Steps

Step 1 ：Multiply both sides of the equation by 2 to get rid of the fraction: \(2 \cdot \frac{5x+9}{2} = 2 \cdot 12\), which simplifies to \(5x + 9 = 24\).

Step 2 ：Subtract 9 from both sides to isolate x: \(5x + 9 - 9 = 24 - 9\), which simplifies to \(5x = 15\).

Step 3 ：Divide both sides by 5 to solve for x: \(\frac{5x}{5} = \frac{15}{5}\), which simplifies to \(x = 3\).

Step 4 ：Substitute x = 3 into the original equation to verify the solution: \(\frac{5 \cdot 3 + 9}{2} = 12\), which holds true.

Step 5 ：Final Answer: \(\boxed{3}\)

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