Answer:
{x | x R, x ≤ 7 5/6 }
Step-by-step explanation:
we have
[tex]x-6\frac{1}{3} \leq 1\frac{1}{2}[/tex]
Convert mixed number to an improper fraction first
[tex]6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}[/tex]
[tex]1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}[/tex]
substitute
[tex]x-\frac{19}{3} \leq \frac{3}{2}[/tex]
Multiply by 6 both sides to remove the fractions
[tex]6x-38 \leq 9[/tex]
Adds 38 both sides
[tex]6x \leq 9+38[/tex]
[tex]6x \leq 47[/tex]
Divide by 6 both sides
[tex]x\leq \frac{47}{6}[/tex]
convert to mixed number
[tex]\frac{47}{6}=\frac{42}{6}+\frac{5}{6}=7\frac{5}{6}[/tex]
substitute
[tex]x\leq 7\frac{5}{6}[/tex]
therefore
{x | x R, x ≤ 7 5/6 }
