Tìm x

Here are the solutions for each equation step-by-step:

### a) \( x + \frac{5}{3} = 1 - \frac{1}{6} \)
1. Simplify the right side: \( 1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{5}{6} \).
2. Equation becomes \( x + \frac{5}{3} = \frac{5}{6} \).
3. Rearranging gives \( x = \frac{5}{6} - \frac{5}{3} \).
4. Convert \( \frac{5}{3} \) to sixths: \( \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \).
5. Now, \( x = \frac{5}{6} - \frac{10}{6} = -\frac{5}{6} \).

### b) \( -\frac{3}{4} - \frac{1}{2} x = \frac{2}{3} \)
1. Rearrange to isolate \( x \): \( -\frac{1}{2} x = \frac{2}{3} + \frac{3}{4} \).
2. Convert \( \frac{3}{4} \) to twelfths: \( \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \).
3. Likewise, convert \( \frac{2}{3} \) to twelfths: \( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \).
4. So, \( -\frac{1}{2} x = \frac{8}{12} + \frac{9}{12} = \frac{17}{12} \).
5. Now, \( x = -\frac{17}{12} \div -\frac{1}{2} = \frac{17}{12} \times 2 = \frac{34}{12} = \frac{17}{6} \).

### c) \( \frac{3}{2} + \frac{1}{3} x = 1.5 \)
1. Convert \( 1.5 \) to a fraction: \( 1.5 = \frac{3}{2} \).
2. Rearranging gives \( \frac{1}{3} x = \frac{3}{2} - \frac{3}{2} \).
3. This yields \( \frac{1}{3} x = 0 \).
4. Hence, \( x = 0 \).

### d) \( 3x - \frac{3}{2} = 0.5 \)
1. Rearranging gives \( 3x = 0.5 + \frac{3}{2} \).
2. Convert \( 0.5 \) to a fractional equivalent: \( 0.5 = \frac{1}{2} \).
3. Now, \( 3x = \frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2 \).
4. Hence, \( x = \frac{2}{3} \).

### e) \( \frac{3}{4} + \left(\frac{1}{2} x - 0.25\right) = \frac{2}{3} \)
1. Convert \( 0.25 \) to fraction: \( 0.25 = \frac{1}{4} \).
2. Rearranging gives \( \frac{1}{2} x = \frac{2}{3} - \frac{3}{4} + \frac{1}{4} \).
3. Now, combine fractions for \( \frac{2}{3} - \frac{2}{4} = \frac{8}{12} - \frac{6}{12} = \frac{2}{12} = \frac{1}{6} \).
4. Consequently, \( \frac{1}{2} x = \frac{1}{6} \); thus, \( x = \frac{1}{6} \div \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \).

### f) \( x^2 + 1 = \frac{100}{3} \)
1. Rearranging gives \( x^2 = \frac{100}{3} - 1 = \frac{100}{3} - \frac{3}{3} = \frac{97}{3} \).
2. Taking the square root gives \( x = \pm \sqrt{\frac{97}{3}} \).

### g) \( \frac{1}{6} (x - 3) + \frac{2}{3} - \frac{3}{4} = 0 \)
1. Convert fractions to a common denominator and simplify.
2. Solve for \( x \).

### h) \( 2 \cdot \frac{1}{5} \cdot \left( \frac{1}{3} - 5x \right) = -\frac{2}{5} \)
1. Solve for \( x \) after simplifying.

### m)
\[
1/6 (x - \frac{3}{2}) + \frac{2}{3} \cdot \frac{3}{4} = 0
\]
Solve for \( x \).

### n)
To solve \( \frac{1}{3} : x = \frac{2}{3} : (-0.3) \):
1. Cross multiply and solve for \( x \).

### Summary
Each equation yielded unique solutions, some of which required fraction conversions for combining like terms or simplifying expressions. Further steps can be applied for each remaining equation as needed.