a)
[tex](x + 20) \div 12 + 68 = 78[/tex]
[tex] \frac{x + 20}{12} + 68 = 78 [/tex]
[tex]x + 20 + 816 = 936[/tex]
[tex]x + 836 = 936[/tex]
[tex]x = 936 - 836[/tex]
[tex]x = 100[/tex]
d)
[tex]101 \times (101 - (101 - 102 \div x)) = 202[/tex]
[tex]101 \times (101 - (101 - \frac{102}{x})) = 202 [/tex]
[tex]101 \times (101 - 101 + \frac{102}{x}) = 202 [/tex]
[tex]101 \times \frac{102}{x} = 202 [/tex]
[tex] \frac{10302}{x} = 202[/tex]
[tex]10302 = 202x[/tex]
[tex]x = 51[/tex]
b)
[tex](x + 282 - 75) \div 2 = 104[/tex]
[tex](x + 207) \div 2 = 104[/tex]
[tex] \frac{x + 207}{2} = 104 [/tex]
[tex]x + 207 = 208[/tex]
[tex]x = 208 - 207[/tex]
[tex]x = 1[/tex]
e)
[tex]369 - ((x + 112) \div 5 + 113) = 434[/tex]
[tex]369 - ( \frac{x + 112}{5} + 113) = 434 [/tex]
[tex]369 - \frac{x + 112}{5} - 113 = 434[/tex]
[tex]256 - \frac{x + 112}{5} = 434[/tex]
[tex]1280 - (x + 112) = 2170[/tex]
[tex]1280 - x - 112 = 2170[/tex]
[tex]1168 - x = 2170[/tex]
[tex] - x = 2170 - 1168[/tex]
[tex] - x = 1002[/tex]
[tex]x = - 1002[/tex]
c)
[tex]x \times 4 \div 10 + 101 = 133[/tex]
[tex] \frac{4}{10}x + 101 = 133 [/tex]
[tex] \frac{2}{5}x + 101 = 133 [/tex]
[tex]2x + 505 = 665[/tex]
[tex]2x = 665 - 505[/tex]
[tex]2x = 160[/tex]
[tex]x = 80[/tex]
f)
[tex]104 \div (( \times - 3 \times 8)2 \div 8) = 13[/tex]
[tex]104((x - 24) \times 2 \div 8) = 13[/tex]
[tex]104 \div \frac{( -x - 24) \times 2}{8} = 13[/tex]
[tex]104 \div \frac{x - 24}{4} = 13[/tex]
[tex]104 \times \frac{4}{x - 24} = 13[/tex]
[tex] \frac{416}{x - 24} = 13 [/tex]
[tex]416 = 13(x - 24)[/tex]
[tex]32 = x - 24[/tex]
[tex] - x = - 24 - 32[/tex]
[tex] - x = - 56[/tex]
[tex]x = 56[/tex]
