Question
Solve $3x – 2 ≡ 0$ (mod $11$)
✓
Answer
$3x – 2 ≡ 0$ (mod $11$)
$3x – 2 = 11$ n for some integer n.
$3x = 11n + 2$
$x=\frac{11 n+2}{3} \text { where } n=2,5,8$
$ x=\frac{11 \times 2+2}{3}=8$
$ x=\frac{11 \times 5+2}{3}$
$ =\frac{55+2}{3}$
$ =\frac{57}{3}$
$ =19$
$ x=\frac{11 \times 8+2}{3}$
$ =\frac{88+2}{3}$
$ =\frac{90}{3}$
$ =30$
$\therefore x = 8, 19, 30, ...$
$3x – 2 = 11$ n for some integer n.
$3x = 11n + 2$
$x=\frac{11 n+2}{3} \text { where } n=2,5,8$
$ x=\frac{11 \times 2+2}{3}=8$
$ x=\frac{11 \times 5+2}{3}$
$ =\frac{55+2}{3}$
$ =\frac{57}{3}$
$ =19$
$ x=\frac{11 \times 8+2}{3}$
$ =\frac{88+2}{3}$
$ =\frac{90}{3}$
$ =30$
$\therefore x = 8, 19, 30, ...$
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