Solve the rational inequality, and write the solution in interval notation.

Question

asked Nov 3, 2023 229k views

1 Answer

Dscarr · Answer 1 · 2023-11-09T02:29:15+0000

We have the next inequality

$(3x-2)/(x-4)\ge2$

we need to rewrite the inequality in standard form

$(3x-2)/(x-4)-2\ge0$

$(3x-2-2\left(x-4\right))/(x-4)\ge0$

$(x+6)/(x-4)\ge0$

then we can identify the intervals

$x\le-6\text{ or }x>4$

in interval notation

$\: (-\infty\: ,\: -6\rbrack\cup\mleft(4,\: \infty\: \mright)$