Question

solve the inequality ( 9x + 1 lt 8x - 2 ). write the solution set in interval notation, and graph it.
the solution set is -3
(type your answer in interval notation )
choose the correct graph of ( 9x + 1 lt 8x - 2 ) below.
a.
b.
c.
d.

Explanation:

Step1: Subtract \(8x\) from both sides

\(9x + 1-8x<8x - 2-8x\)
\(x + 1<-2\)

Step2: Subtract \(1\) from both sides

\(x+1 - 1<-2 - 1\)
\(x<-3\)

In interval notation, the solution set for \(x < - 3\) is \((-\infty,-3)\)

For the graph:

• The inequality \(x < - 3\) means we have an open circle at \(x=-3\) (since the inequality is strict, \(x

eq - 3\)) and the arrow points to the left (towards more negative values)

Answer:

The solution set in interval notation is \((-\infty,-3)\).
For the graph, option A (assuming in option A there is an open - circle at \(-3\) and the arrow points to the left) is correct.