Solve for $$ w $$. $$ \frac{11 w}{10}-2=\frac{9 w}{8} $$ Simplify, your answer as much as possible.

Question

UpStudy AI · Accepted Answer

To solve the equation for $$ w $$:

$$
\frac{11w}{10} - 2 = \frac{9w}{8}
$$

**Step 1: Eliminate the Fractions**

Find the least common multiple (LCM) of the denominators 10 and 8, which is 40. Multiply every term by 40 to eliminate the fractions:

$$
40 \times \left(\frac{11w}{10}\right) - 40 \times 2 = 40 \times \left(\frac{9w}{8}\right)
$$

**Step 2: Simplify Each Term**

$$
4 \times 11w - 80 = 5 \times 9w
$$
$$
44w - 80 = 45w
$$

**Step 3: Isolate $$ w $$**

Subtract $$ 44w $$ from both sides:

$$
-80 = 45w - 44w
$$
$$
-80 = w
$$

**Solution:**

$$
w = -80
$$
$$ w = -80 $$

Solve for \( w \). \[ \frac{11 w}{10}-2=\frac{9 w}{8} \] Simplify, your answer as much as possible.