Questions: Solve for (x). [ frac23-frac5x+3=frac13 x+9 x= ]

$Solve for (x). [ frac23-frac5x+3=frac13 x+9 x= ]$

Transcript text: Solve for $x$. \[ \begin{array}{l} \frac{2}{3}-\frac{5}{x+3}=\frac{1}{3 x+9} \\ x= \end{array} \] Question Help: Video eBook Written Example Submit Question

Solution

Solution Steps

To solve the equation $\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9}$, we can follow these steps:

Recognize that $3x + 9$ can be factored as $3(x + 3)$.
Rewrite the equation with a common denominator.
Solve the resulting equation for $x$.

Step 1: Recognize the Common Denominator

We start with the equation: \[ \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9} \] Notice that $3x + 9$ can be factored as $3(x + 3)$.

Step 2: Rewrite the Equation

Rewrite the equation with a common denominator: \[ \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3(x+3)} \]

Step 3: Clear the Denominators

Multiply both sides by $3(x + 3)$ to clear the denominators: \[ 2(x + 3) - 15 = 1 \]

Step 4: Simplify and Solve for $x$

Simplify the equation: \[ 2x + 6 - 15 = 1 \] \[ 2x - 9 = 1 \] \[ 2x = 10 \] \[ x = 5 \]

Final Answer

$\boxed{x = 5}$

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