Answer
$(-\infty,1)$
Work Step by Step
$\frac{x}{6}+\frac{3x-2}{2}\lt\frac{2}{3}$
Multiply both sides by 6, the least common multiple, so eliminate fractions.
$6(\frac{x}{6})+6(\frac{3x-2}{2})\lt6(\frac{2}{3})$
$x+3(3x-2)\lt\frac{12}{3}$
$x+9x-6\lt4$
Combine like terms.
$10x-6\lt4$
Add 6 to both sides.
$10x-6+6\lt4+6$
$10x\lt10$
Divide both sides by 10.
$10x\div10\lt10\div10$
$x\lt1$
This is written in interval notation as
$(-\infty,1)$
where ) indicates that the solution set for x approaches 1 but does not include 1.
