Questions: 1/3 x-6=1/8 x+4 The solution is x= (Type an integer or a simplified fraction.)

$1/3 x-6=1/8 x+4 The solution is x= (Type an integer or a simplified fraction.)$

Transcript text: \[ \frac{1}{3} x-6=\frac{1}{8} x+4 \] The solution is $x=$ $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

To solve the equation $\frac{1}{3} x - 6 = \frac{1}{8} x + 4$, we need to isolate $x$ on one side of the equation. We can do this by first eliminating the fractions through finding a common denominator, then moving all terms involving $x$ to one side and constant terms to the other. Finally, solve for $x$ by simplifying the equation.

Step 1: Set Up the Equation

We start with the equation: \[ \frac{1}{3}x - 6 = \frac{1}{8}x + 4 \]

Step 2: Eliminate Fractions

To eliminate the fractions, we find a common denominator, which is 24. Multiply every term by 24: \[ 24 \left(\frac{1}{3}x\right) - 24 \cdot 6 = 24 \left(\frac{1}{8}x\right) + 24 \cdot 4 \] This simplifies to: \[ 8x - 144 = 3x + 96 \]

Step 3: Isolate the Variable

Subtract $3x$ from both sides to get all terms involving $x$ on one side: \[ 8x - 3x - 144 = 96 \] Simplify: \[ 5x - 144 = 96 \]

Step 4: Solve for $x$

Add 144 to both sides to isolate the term with $x$: \[ 5x = 240 \] Divide both sides by 5 to solve for $x$: \[ x = 48 \]