Question
What is the solution to inequality?
Answers
GPT-4o mini
To provide a solution for an inequality, I first need to know the specific inequality you are asking about. Inequalities can take various forms, such as linear inequalities, quadratic inequalities, or others, and the methods for solving them can differ accordingly.
For example:
1. **Linear Inequality**:
- If you have an inequality like \(2x + 3 < 7\), you would first subtract 3 from both sides:
\[
2x < 4
\]
Then, divide both sides by 2:
\[
x < 2
\]
- The solution set is all \(x\) values that are less than 2.
2. **Quadratic Inequality**:
- For an inequality like \(x^2 - 4 > 0\), you would first find the corresponding equation \(x^2 - 4 = 0\) which factors to \((x - 2)(x + 2) = 0\). This gives roots at \(x = -2\) and \(x = 2\).
- Testing intervals around these roots (for example, testing numbers in the intervals \((- \infty, -2)\), \((-2, 2)\), and \((2, \infty)\)), you can find where the quadratic is positive. In this case, the solution would be \(x < -2\) or \(x > 2\).
Please provide the specific inequality you want to solve, and I can guide you through the solution process!
For example:
1. **Linear Inequality**:
- If you have an inequality like \(2x + 3 < 7\), you would first subtract 3 from both sides:
\[
2x < 4
\]
Then, divide both sides by 2:
\[
x < 2
\]
- The solution set is all \(x\) values that are less than 2.
2. **Quadratic Inequality**:
- For an inequality like \(x^2 - 4 > 0\), you would first find the corresponding equation \(x^2 - 4 = 0\) which factors to \((x - 2)(x + 2) = 0\). This gives roots at \(x = -2\) and \(x = 2\).
- Testing intervals around these roots (for example, testing numbers in the intervals \((- \infty, -2)\), \((-2, 2)\), and \((2, \infty)\)), you can find where the quadratic is positive. In this case, the solution would be \(x < -2\) or \(x > 2\).
Please provide the specific inequality you want to solve, and I can guide you through the solution process!