a)
[tex] \frac{1}{2} \times x - \frac{1}{3} = \frac{1}{3} \times x[/tex]
[tex] \frac{x}{2} - \frac{1}{3} = \frac{x}{3} [/tex]
[tex] \frac{3x - 2}{6} = \frac{2x}{6} [/tex]
[tex]3x - 2 = 2x[/tex]
[tex]3x - 2x = 2[/tex]
[tex]x = 2[/tex]
b)
[tex] \frac{1}{2} ( \frac{1}{2} ( \frac{x}{2} - 1) - 1) + 1 = \frac{5}{4} [/tex]
[tex] \frac{1}{2} ( \frac{1}{2} \times \frac{x - 2}{2} - 1) + 1 = \frac{5}{4} [/tex]
[tex] \frac{1}{2} ( \frac{x - 2}{4} - 1) + 1 = \frac{5}{4} [/tex]
[tex] \frac{1}{2} \times \frac{x - 2 - 4}{4} + 1 = \frac{5}{4} [/tex]
[tex] \frac{1}{2} \times \frac{x - 6}{4} = \frac{5 - 4}{4} [/tex]
[tex] \frac{x - 6}{8} = \frac{1}{4} [/tex]
[tex]4 \times (x - 6) = 8[/tex]
[tex]4x - 24 = 8[/tex]
[tex]x = 8[/tex]
