a)
[tex]6 \div (20 \times 5 - (a \div 3 - 45 \div 5) - 22) = 1[/tex]
[tex]6 \div (100 - ( \frac{1}{3}a - 9) - 22) = 1 [/tex]
[tex]6 \div (100 - \frac{1}{3}a + 9 - 22) = 1[/tex]
[tex]6 \div (87 - \frac{1}{3} a) = 1[/tex]
[tex]6 \div \frac{261 - a}{3} = 1 [/tex]
[tex] \frac{18}{261 - a} = 1[/tex]
[tex]18 = 261 - a[/tex]
[tex]a = 261 - 18[/tex]
[tex]a = 243[/tex]
b)
[tex](1 + 2 \times (6 + a \div 3) - 5) \div 6= 2[/tex]
[tex](1 + 2 \times (6 + \frac{1}{3} a) - 5) \times \frac{1}{6} = 2 [/tex]
[tex](1 + 12 + \frac{2}{3} a - 5) \times \frac{1}{6} = 2 [/tex]
[tex](8 + \frac{2}{3}a) \times \frac{1}{6} = 2[/tex]
[tex] \frac{24 + 2a}{3} \times \frac{1}{6} = 2 [/tex]
[tex] \frac{12 + a}{ 3} \times \frac{1}{3} = 2[/tex]
[tex] \frac{12 + a}{9} = 2 [/tex]
[tex]12 + a = 18[/tex]
[tex]a = 18 - 12[/tex]
[tex]a = 6[/tex]
c)
[tex]2 + 2 \times (2 + 3 \times (2 + 404 \div a) - 612 \div 6) = 420[/tex]
[tex]2 + 2 \times (2 + 3 \times (2 + \frac{404}{a}) - 102) = 420 [/tex]
[tex]2 + 2 \times (2 + 6 + \frac{1212}{a} - 102) = 420[/tex]
[tex]2 + 2 \times ( - 94 + \frac{1212}{a}) = 420[/tex]
[tex]2 - 188 + \frac{2424}{a} = 420 [/tex]
[tex] - 186 + \frac{2424}{a} = 420 [/tex]
[tex] \frac{2424}{a} = 420 + 186 [/tex]
[tex] \frac{2424}{a} = 606 [/tex]
[tex]2424 = 606a[/tex]
[tex]606 = 2424[/tex]
[tex]a = 4[/tex]
d)
[tex]36 \times 2 + ((136 \times 4 + x \div 6) \times 5 - 2670) = 167[/tex]
[tex]72 + ((544 + \frac{1}{6}x) \times 5 - 2670) = 167[/tex]
[tex]72 + (2720 + \frac{5}{6} x - 2670) = 167[/tex]
[tex]72 + (50 + \frac{5}{6} x) = 167[/tex]
[tex]72 + 50 + \frac{5}{6}x = 167[/tex]
[tex]122 + \frac{5}{6}x = 167 [/tex]
[tex]732 + 5x = 1002[/tex]
[tex]5x = 1002 - 732[/tex]
[tex]5x = 270[/tex]
[tex]x = 54[/tex]
