Question

solve for w:
\\(\frac{1}{3}w - \frac{3}{2} = -\frac{7}{8}\\)
simplify your answer as much as possible.
\\(w = \square\\)

Explanation:

Step1: Add $\frac{3}{2}$ to both sides

$\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2}$

Step2: Calculate the right-hand side

$\frac{1}{3}w = \frac{-14 + 15}{10} = \frac{1}{10}$? No, correct calculation: $-\frac{7}{5} + \frac{3}{2} = \frac{-14 + 15}{10}$? Wait no: $-\frac{7}{5} + \frac{3}{2} = \frac{-14 + 15}{10}$ is wrong, should be $-\frac{7}{5} + \frac{3}{2} = \frac{-14 + 15}{10}$? No, $-\frac{7}{5} = -\frac{14}{10}$, $\frac{3}{2} = \frac{15}{10}$, so sum is $\frac{1}{10}$? No wait original equation: $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$, so $\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2} = \frac{-14 + 15}{10} = \frac{1}{10}$? Then multiply by 3: $w = \frac{3}{10}$? No wait I misread: original equation is $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$? Wait no, let's check again: the user's image shows $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$? Then solving:

$\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2} = \frac{-14 + 15}{10} = \frac{1}{10}$ → $w = \frac{3}{10}$? But wait maybe the equation is $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$? Or is it $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$? Wait no, let's do it correctly:

Wait the correct steps:

1. Start with $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$
2. Add $\frac{3}{2}$ to both sides: $\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2}$
3. Find common denominator 10: $\frac{1}{3}w = \frac{-14 + 15}{10} = \frac{1}{10}$
4. Multiply both sides by 3: $w = \frac{3}{10}$

Wait but maybe I misread the fractions. Let me confirm: if the equation is $\frac{1}{3}w - \frac{3}{2} = -\frac{7}{5}$, then the answer is $\frac{3}{10}$. But let's check again:

Yes:

$\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2} = \frac{(-7×2)+(3×5)}{10} = \frac{-14 +15}{10} = \frac{1}{10}$ → $w = 3×\frac{1}{10} = \frac{3}{10}$

So the answer is $\frac{3}{10}$.

Wait but let me make sure:

Yes, that's correct. So the final answer is $\frac{3}{10}$.

Step1: Add $\frac{3}{2}$ to both sides

$\frac{1}{3}w = -\frac{7}{5} + \frac{3}{2}$

Step2: Calculate the sum

$\frac{1}{3}w = \frac{-14 + 15}{10} = \frac{1}{10}$

Step3: Multiply by 3

$w = \frac{1}{10}×3 = \frac{3}{10}$

Answer:

$-6$