Question

Graph the solution set of the inequality and write the solution using interval notation.

Answer 1

Consider the following inequality:

`-4<(3x-2)/(5)\leq6`

this is equivalent to:

`(-4)(5)<3x-2\leq(6)(5)`

this is equivalent to:

`-20<3x-2\leq30`

solving for 3x, this is equivalent to:

`-20+2<3x\leq30+2`

this is equivalent to:

`-18<3x\leq32`

solving for x, we get:

`-(18)/(3)this is equivalent to:<p></p><p></p>[tex]-6<p>in interval notation,<strong> </strong><strong>this is equivalent to:</strong></p><p></p>[tex](-6,(32)/(3)\rbrack`

the solution set on the real line is: