Question
Which graph represents the solution to the inequality? -2.4(x - 7) > 74.4?
Answers
GPT-4o mini
To solve the inequality \(-2.4(x - 7) > 74.4\), let's start by simplifying it.
1. Distribute \(-2.4\):
\[
-2.4x + 16.8 > 74.4
\]
2. Subtract \(16.8\) from both sides:
\[
-2.4x > 74.4 - 16.8
\]
\[
-2.4x > 57.6
\]
3. Divide both sides by \(-2.4\). Remember that when you divide by a negative number, you must flip the inequality sign:
\[
x < \frac{57.6}{-2.4}
\]
\[
x < -24
\]
The solution to the inequality is \(x < -24\).
To graph this solution:
- Draw a number line.
- Locate -24 on the number line.
- Since this is a "less than" inequality, you would use an open circle at -24 (to indicate that -24 is not included) and shade to the left of -24 to indicate that the solution includes all numbers less than -24.
In summary, the correct graph would show an open circle at \(-24\) with shading to the left. If you have multiple graphs to choose from, look for one that matches this description.
1. Distribute \(-2.4\):
\[
-2.4x + 16.8 > 74.4
\]
2. Subtract \(16.8\) from both sides:
\[
-2.4x > 74.4 - 16.8
\]
\[
-2.4x > 57.6
\]
3. Divide both sides by \(-2.4\). Remember that when you divide by a negative number, you must flip the inequality sign:
\[
x < \frac{57.6}{-2.4}
\]
\[
x < -24
\]
The solution to the inequality is \(x < -24\).
To graph this solution:
- Draw a number line.
- Locate -24 on the number line.
- Since this is a "less than" inequality, you would use an open circle at -24 (to indicate that -24 is not included) and shade to the left of -24 to indicate that the solution includes all numbers less than -24.
In summary, the correct graph would show an open circle at \(-24\) with shading to the left. If you have multiple graphs to choose from, look for one that matches this description.