Question

How do I solve and graph this inequality?-(x + 6) > - 2 ( 1 - x)

Answer 1

The question is given below as

`-(x+6)>-2(1-x)`

Step 1:

Expand the brackets

`\begin{gathered} -(x+6)>-2(1-x) \\ -x-6>-2+2x \end{gathered}`

Step 2:

Collect similar terms

`\begin{gathered} -x-6>-2+2x \\ -x-2x>-2+6 \\ -3x>4 \end{gathered}`

Step 3:

Divide both sides by -3 (note: when divided by a negative coefficient, the inequality sign will be reversed)

`\begin{gathered} (-3x)/(-3)>(4)/(-3) \\ x<-(4)/(3) \end{gathered}`

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)