the following inequality and graph the solution.

Question

seven ninths x greater than or equals 1
7
9x≥1
Question content area bottom
Part 1
Select the correct choice and fill in the answer box to complete your choice.
A.
xless than<enter your response here
B.
xgreater than or equals≥enter your response here
C.
xgreater than>enter your response here
D.
xless than or equals≤enter your response here

Answer 1

To solve the inequality \(\frac{7}{9}x \geq 1\), we will first isolate \(x\).

1. Multiply both sides of the inequality by \(9\) to eliminate the fraction:

   \[ 7x \geq 9 \]

2. Next, divide both sides by \(7\):

   \[ x \geq \frac{9}{7} \]

So the solution to the inequality is:

\[ x \geq \frac{9}{7} \]

Now, let's fill in the answer box in your choices:

The correct choice is: B. \(x \geq \frac{9}{7}\)

Graphing the Solution

To graph this solution on a number line:

1. Draw a number line.
2. Locate \(\frac{9}{7}\), which is approximately \(1.2857\).
3. Since the inequality includes "greater than or equal to", draw a closed circle (or a filled dot) at \(\frac{9}{7}\).
4. Shade the line to the right of this point, indicating that \(x\) can take any value greater than \(\frac{9}{7}\).

This graph represents all the values of \(x\) that satisfy the inequality.