Gquations Watch the video and then solve the problem given below. Click here to watch the video. For the following equation, a. Write the value or values of the variable that \( m \) \( \frac{2}{9 x}+\frac{1}{4}=\frac{67}{18 x}-\frac{1}{3} \)

Sure, let's solve the given equation step by step. ### **Given Equation:** \[ \frac{2}{9x} + \frac{1}{4} = \frac{67}{18x} - \frac{1}{3} \] ### **Step 1: Eliminate Fractions by Finding a Common Denominator** To simplify the equation, it's helpful to eliminate the fractions by finding a common denominator. The denominators in this equation are \(9x\), \(4\), \(18x\), and \(3\). The least common multiple (LCM) of these denominators is \(36x\). ### **Step 2: Multiply Each Term by the LCM (36x) to Eliminate the Denominators** \[ 36x \times \left(\frac{2}{9x}\right) + 36x \times \left(\frac{1}{4}\right) = 36x \times \left(\frac{67}{18x}\right) - 36x \times \left(\frac{1}{3}\right) \] Simplifying each term: \[ \frac{36x \times 2}{9x} + \frac{36x \times 1}{4} = \frac{36x \times 67}{18x} - \frac{36x \times 1}{3} \] \[ 8 + 9x = 134 - 12x \] ### **Step 3: Collect Like Terms** Bring all terms involving \(x\) to one side and constant terms to the other side: \[ 9x + 12x = 134 - 8 \] \[ 21x = 126 \] ### **Step 4: Solve for \(x\)** \[ x = \frac{126}{21} = 6 \] ### **Solution:** \[ \boxed{6} \]