Question

Solve for xx and graph the solution on the number line below.
minus, 8, is greater than or equal to, minus, 8, x
−8≥
−8x

Answer 1

To solve for \( x \) in the inequality \( -8 \geq -8x \), we can start by isolating \( x \). Here are the steps:

1. Since we want to solve for \( x \), we want to get \( x \) by itself on one side of the inequality. We can do this by dividing both sides by -8.

2. Remember that when you divide by a negative number in an inequality, you must reverse the inequality sign. Here, we are dividing by -8 (a negative), so the inequality will change from 'greater than or equal to' to 'less than or equal to'.

The division step gives us:

\( \frac{-8}{-8} \leq \frac{-8x}{-8} \)

Which simplifies to:

\( 1 \leq x \)

The solution to the inequality is \( x \geq 1 \), which means any number greater than or equal to 1 will satisfy the inequality.

Now for the graph on the number line:

```plaintext
-----------------------------•====>
0 1
```

The dark circle at 1 represents that 1 is included in the solution (since it's 'greater than or equal to'), and the line continues to the right, indicating that all numbers greater than 1 are also included in the solution set.