Question

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Explanation:

6.

Step1: Draw a number line

Draw a straight line and mark points \(0,1,2,3,4,\cdots\) on it.

Step2: Graph the solution \(x > 3\)

Since \(x>3\), we use an open circle at \(x = 3\) (because \(3\) is not included in the solution set) and draw an arrow to the right of \(3\) to represent all the numbers greater than \(3\).

7.

The graph has a closed circle at \(x = 2\) (which means \(2\) is included in the solution set) and an arrow to the right. So the inequality is \(x\geq2\).

8.

Step1: Divide by the smallest prime number

Start with \(360\div2 = 180\).

Step2: Continue dividing

\(180\div2=90\), \(90\div2 = 45\).

Step3: Divide by the next prime number

Since \(45\) is odd, divide by \(3\): \(45\div3=15\), \(15\div3 = 5\).

Step4: Write as a product of prime factors

Since \(5\) is a prime number, \(360=2\times2\times2\times3\times3\times5=2^{3}\times3^{2}\times5\).

Answer:

1. Graph with open - circle at \(3\) and arrow to the right.
2. \(x\geq2\)
3. \(360 = 2^{3}\times3^{2}\times5\)