Questions: Solve the equation. 14y/15 - 9 = 8 - 5y/3 y = □

Solve the equation. 14y/15 - 9 = 8 - 5y/3 y = □
Transcript text: Solve the equation. \[ \frac{14 y}{15}-9=8-\frac{5 y}{3} \] \[ \mathrm{y}=\square \]
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Solution

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Solution Steps

Step 1: Move all terms involving \( y \) to one side and constants to the other

\[ \frac{14 y}{15} + \frac{5 y}{3} = 8 + 9 \]

Step 2: Combine like terms

To combine \(\frac{14 y}{15}\) and \(\frac{5 y}{3}\), first convert \(\frac{5 y}{3}\) to a denominator of 15: \[ \frac{5 y}{3} = \frac{25 y}{15} \] Now add the terms: \[ \frac{14 y}{15} + \frac{25 y}{15} = \frac{39 y}{15} \] Simplify the right-hand side: \[ 8 + 9 = 17 \]

Step 3: Solve for \( y \)

\[ \frac{39 y}{15} = 17 \] Multiply both sides by 15: \[ 39 y = 255 \] Divide both sides by 39: \[ y = \frac{255}{39} \] Simplify the fraction: \[ y = \frac{85}{13} \]

Final Answer

\(\boxed{y = \frac{85}{13}}\)

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