Answer:
[tex]x\le \:-\frac{8}{3}[/tex]
[tex]x>4[/tex]
Step-by-step explanation:
[tex]\frac{3x+8}{x-4}\ge \:0[/tex]
Multiply both sides by (x - 4).
[tex]\frac{3x+8}{x-4} (x-4) \ge \:0(x-4)[/tex]
[tex]3x+8\leq \:0[/tex]
[tex]3x+8-8\leq \:0-8[/tex]
[tex]3x \leq \:-8[/tex]
[tex]x\le \:-\frac{8}{3}[/tex]
Makes denominator equal to 0.
[tex]x-4=0[/tex]
[tex]x = 4[/tex]
[tex]-8/3 \leq x<4[/tex] doesn't work in the original inequality.
[tex]x>4[/tex] works in the original inequality.
