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:

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

Answer:

`((2)/(3),(14)/(3))\text{.}`