Question

Use the interval notation to represent all values of ex satisfying the given conditions.

Answer 1

Notice that solving the given problem is equivalent to solving

$|3x-8|+2<8,$

for x.

Adding -2 to both sides of inequality we get:

$|3x-8|<8-2=6.$

Now, recall that:

$|a|Therefore, we can rewrite the last inequality as:[tex]-6<3x-8<6.$

Adding 8 we get:

$\begin{gathered} -6+8<3x-8+8<6+8, \\ 2<3x<14. \end{gathered}$

Finally, dividing by 3, we get:

$\frac{2}{3}The above result in interval notation is:[tex](\frac{2}{3},\frac{14}{3})\text{.}$

Answer:

$(\frac{2}{3},\frac{14}{3})\text{.}$