Question

Solve 9abs(3n-2) + 6 > 51 and graph on the number line

Answer 1

Solving the inequality,

`\begin{gathered} 9\lvert3n-2\rvert+6>51 \\ \rightarrow9\lvert3n-2\rvert>45 \\ \rightarrow\lvert3n-2\rvert>5 \end{gathered}`

Remember that if

`\lvert u\rvert>a,a>0\Rightarrow u<-a\text{ or }u>a`

This way, we get:

`\begin{gathered} 3n-2<-5\rightarrow3n<-3\rightarrow n<-1 \\ 3n-2>5\rightarrow3n>7\rightarrow n>(7)/(3) \end{gathered}`

As an interval, we get:

`\: \mleft(-\infty\: ,\: -1\mright)\cup\mleft((7)/(3),\: \infty\: \mright)`

In the number line, we get: