Question

solve the given inequality. write the solution set using interval notation, then graph it. 5x - 9 > 11. the solution set is (-∞,4. (give your answer in interval notation.) graph the solution set on the number line.

Explanation:

Step1: Isolate the variable term

Add 9 to both sides of the inequality \(5x - 9>11\). We get \(5x-9 + 9>11 + 9\), which simplifies to \(5x>20\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(5x>20\) by 5. Since 5 is positive, the direction of the inequality sign remains the same. So \(\frac{5x}{5}>\frac{20}{5}\), and \(x > 4\).

Step3: Write in interval - notation

The solution in interval notation is \((4,\infty)\).

Step4: Graph on number - line

Draw a number - line. Mark a open circle at 4 (because 4 is not included in the solution set \(x>4\)) and shade the line to the right of 4 to represent all the numbers greater than 4.

Answer:

The solution set in interval notation is \((4,\infty)\). On the number - line, there is an open circle at 4 and the line is shaded to the right of 4.