Question

Which graph shows the solution set for Negative 1.1 x + 6.4 greater-than negative 1.3?
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the left of the circle is shaded.
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the right of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the left of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the right of the circle is shaded.

Answer 1

To solve the inequality \(-1.1x + 6.4 > -1.3\), we can first isolate \(x\):

1. Subtract 6.4 from both sides:

\[
-1.1x > -1.3 - 6.4
\]
\[
-1.1x > -7.7
\]

2. Now, divide both sides by -1.1. Remember, when we divide by a negative number, we need to flip the inequality sign:

\[
x < \frac{-7.7}{-1.1}
\]
\[
x < 7
\]

Now, we understand the inequality indicates that \(x\) must be less than 7.

In terms of a number line graph, we have:

- An open circle at 7 (since 7 is not included in the solution set, we use an open circle)
- Shading to the left of 7, indicating all numbers less than 7 are included.

Among the options provided, the correct answer is:

**A number line going from 0 to 10. An open circle is at 7. Everything to the left of the circle is shaded.**