Questions: Solve for (x) : [ frac72 x+frac74=2+frac16 x x= ]

$Solve for (x) : [ frac72 x+frac74=2+frac16 x x= ]$

Transcript text: Solve for $x$ : \[ \begin{array}{l} \frac{7}{2} x+\frac{7}{4}=2+\frac{1}{6} x \\ x= \end{array} \]

Solution

Solution Steps

Step 1: Set Up the Equation

We start with the given equation: \[ \frac{7}{2}x + \frac{7}{4} = 2 + \frac{1}{6}x \]

Step 2: Eliminate Fractions

To eliminate the fractions, multiply every term by the least common multiple of the denominators, which is 12: \[ 12 \left(\frac{7}{2}x\right) + 12 \left(\frac{7}{4}\right) = 12 \cdot 2 + 12 \left(\frac{1}{6}x\right) \] This simplifies to: \[ 42x + 21 = 24 + 2x \]

Step 3: Combine Like Terms

Subtract $2x$ from both sides to combine like terms: \[ 42x - 2x + 21 = 24 \] This simplifies to: \[ 40x + 21 = 24 \]

Step 4: Isolate the Variable

Subtract 21 from both sides to isolate the term with $x$: \[ 40x = 24 - 21 \] This simplifies to: \[ 40x = 3 \]

Step 5: Solve for $x$

Divide both sides by 40 to solve for $x$: \[ x = \frac{3}{40} = 0.0750 \]