Question

How do you do this question?

Answer 1

Answer:

x={1,2,3}

Step-by-step explanation:

The given inequality is

$1 \leqslant \frac{6x - 1}{3} \: < \: 7$

We multiply through by the LCM of 3 to get:

$3\leqslant 6x - 1\: < \: 21$

We add 1 to both sides to get:

$3 + 1\leqslant 6x \: < \: 21 + 1$

$4\leqslant 6x \: < \: 22$

Divide through by 6 to get:

$\frac{4}{6} \leqslant x \: < \: \frac{22}{6}$

This gives us:

$\frac{2}{3} \leqslant x \: < \: \frac{11}{3}$

$0.67 \leqslant x \: < \:3.67$

Since x is an integer, the possible values are:

x={1,2,3}