Question

solve for (w).

-\frac{2}{w} = 6

simplify your answer as much as possible.

Explanation:

🆕 New Concept Discovered: Solving Rational Equations
Isolating a variable in the denominator

Step 1: Clear the fraction

To get the variable \( w \) out of the denominator, multiply both sides of the equation by \( w \):

$$ -\frac{2}{w} \cdot w = 6 \cdot w $$

$$ -2 = 6w $$

Step 2: Isolate the variable

Divide both sides by \( 6 \) to solve for \( w \):

$$ w = \frac{-2}{6} $$

Step 3: Simplify the fraction

Reduce the fraction to its simplest form by dividing the numerator and the denominator by their greatest common divisor, which is \( 2 \):

$$ w = -\frac{1}{3} $$

Answer:

$$ w = -\frac{1}{3} $$