Solution:
The question is given below as
[tex]-(x+6)>-2(1-x)[/tex]
Step 1:
Expand the brackets
[tex]\begin{gathered} -(x+6)>-2(1-x) \\ -x-6>-2+2x \end{gathered}[/tex]
Step 2:
Collect similar terms
[tex]\begin{gathered} -x-6>-2+2x \\ -x-2x>-2+6 \\ -3x>4 \end{gathered}[/tex]
Step 3:
Divide both sides by -3 (note: when divided by a negative coefficient, the inequality sign will be reversed)
[tex]\begin{gathered} \frac{-3x}{-3}>\frac{4}{-3} \\ x<-\frac{4}{3} \end{gathered}[/tex]
Hence,
The solution for the inequality is x < -4/3
The number line is given below as
While the graph is given below ( it will be graphed with a broken line)
