Question

this question has two parts. first, answer part a. then, answer part b.
part a
solve the inequality ( 2>\frac{x}{4} ) and write the solution in set - builder notation.
part b
graph the solution on a number line.

Explanation:

Step1: Solve the inequality

Multiply both sides of \(2>\frac{x}{4}\) by \(4\) (since \(4>0\), the inequality sign remains the same).
\(2\times4>\frac{x}{4}\times4\)
\(8 > x\), which can be rewritten as \(x<8\).
In set - builder notation, this is \(\{x|x < 8\}\).

Step2: Graph the solution

For the inequality \(x < 8\), we have an open circle at \(x = 8\) (because \(8\) is not included in the solution set) and the arrow points to the left (towards smaller values of \(x\)).

Answer:

• Part A: \(\{x|x < 8\}\)
• Part B: An open circle at \(8\) on the number line with an arrow pointing to the left.