Sure, I'll help you solve these equations.

### Equation (e):
\[ x \left( \frac{17}{2} - \left( -\frac{3}{7} + \frac{5}{3} \right) \right) = -\frac{1}{3} \]

First, simplify the expression inside the parentheses:
\[ -\frac{3}{7} + \frac{5}{3} \]

To add these fractions, find a common denominator. The least common multiple of 7 and 3 is 21:
\[ -\frac{3}{7} = -\frac{3 \times 3}{7 \times 3} = -\frac{9}{21} \]
\[ \frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21} \]

Now add the fractions:
\[ -\frac{9}{21} + \frac{35}{21} = \frac{35 - 9}{21} = \frac{26}{21} \]

So the equation becomes:
\[ x \left( \frac{17}{2} - \frac{26}{21} \right) = -\frac{1}{3} \]

Next, find a common denominator for the fractions inside the parentheses. The least common multiple of 2 and 21 is 42:
\[ \frac{17}{2} = \frac{17 \times 21}{2 \times 21} = \frac{357}{42} \]
\[ \frac{26}{21} = \frac{26 \times 2}{21 \times 2} = \frac{52}{42} \]

Now subtract the fractions:
\[ \frac{357}{42} - \frac{52}{42} = \frac{357 - 52}{42} = \frac{305}{42} \]

So the equation is now:
\[ x \left( \frac{305}{42} \right) = -\frac{1}{3} \]

Solve for \( x \):
\[ x = -\frac{1}{3} \div \frac{305}{42} = -\frac{1}{3} \times \frac{42}{305} = -\frac{42}{915} = -\frac{14}{305} \]

### Equation (f):
\[ \frac{9}{2} - \left[ \frac{2}{3} - \left( x + \frac{7}{4} \right) \right] = \frac{5}{4} \]

First, simplify the expression inside the parentheses:
\[ \frac{2}{3} - \left( x + \frac{7}{4} \right) \]

To subtract these, find a common denominator. The least common multiple of 3 and 4 is 12:
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
\[ \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \]

So the expression becomes:
\[ \frac{8}{12} - \left( x + \frac{21}{12} \right) = \frac{8}{12} - x - \frac{21}{12} = -x + \frac{8 - 21}{12} = -x - \frac{13}{12} \]

Now the equation is:
\[ \frac{9}{2} - \left( -x - \frac{13}{12} \right) = \frac{5}{4} \]

Simplify the equation:
\[ \frac{9}{2} + x + \frac{13}{12} = \frac{5}{4} \]

Find a common denominator for the fractions. The least common multiple of 2, 12, and 4 is 12:
\[ \frac{9}{2} = \frac{9 \times 6}{2 \times 6} = \frac{54}{12} \]
\[ \frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12} \]

So the equation becomes:
\[ \frac{54}{12} + x + \frac{13}{12} = \frac{15}{12} \]

Combine the fractions on the left side:
\[ \frac{54 + 13}{12} + x = \frac{15}{12} \]
\[ \frac{67}{12} + x = \frac{15}{12} \]

Subtract \(\frac{67}{12}\) from both sides:
\[ x = \frac{15}{12} - \frac{67}{12} \]
\[ x = \frac{15 - 67}{12} \]
\[ x = \frac{-52}{12} \]
\[ x = -\frac{13}{3} \]

So the solutions are:
\[ x = -\frac{14}{305} \]
\[ x = -\frac{13}{3} \]