Solve $\frac{2}{3} (x - 1) + 4 < 10$ and represent its solution on a number line. Given replacement set is $- 8, - 6, - 4, 3, 6, 8, 12$ .

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Solution

$\frac{2}{3} (x - 1) + 4 < 10$
$\frac{2}{3} x - \frac{2}{3} + 4 < 10$
$\frac{2}{3} x < 10 - 4 + \frac{2}{3}$
$\frac{2}{3} x < 6 + \frac{2}{3}$
$\frac{2}{3} x < \frac{20}{3}$
$x < \frac{20}{3} \div \frac{2}{3}$
$x < \frac{20}{3} \times \frac{3}{2}$
$x < 10$
Given that the set $x$ is a sub set of replacement set ${- 8, - 6, - 4, 3, 6, 8, 12}$
Ans: set $x$ = ${- 8, - 6, - 4, 3, 6, 8}$
Hence the number of integers in the set $x$ is 6

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