Question

solve the linear inequality. other than \\( \varnothing \\), use interval notation to express the solution set and graph the solution set on a number line.\\( 3x - 2 > 2x - 1 \\)\\( \bigcirc \\ (1, \infty) \\)\\( \bigcirc \\ (-3, \infty) \\)\\( \bigcirc \\ 1, \infty) \\)\\( \bigcirc \\ (-infty, 1 \\)

Explanation:

Step1: Subtract $2x$ from both sides

$3x - 2 - 2x > 2x - 1 - 2x$
$x - 2 > -1$

Step2: Add 2 to both sides

$x - 2 + 2 > -1 + 2$
$x > 1$

Step3: Write in interval notation

For $x > 1$, the interval is $(1, \infty)$, with an open circle at 1 and shading to the right on the number line.

Answer:

(1, ∞)
(With a number line showing an open circle at 1 and the line shaded to the right, matching the first option's graph)