Find all real numbers  such that . Give your answer as an interval.


It seems like there might have been a slight miscommunication in your request. Let's clarify the type of inequality you are interested in solving. Since your original question involved an inequality, I will assume you want to solve another inequality. I'll create an example for you.

Let's solve the inequality:
\[ 4 - 3x \leq 2x + 7 \]

Here are the steps:

1. Subtract \(2x\) from both sides:
   \[ 4 - 3x - 2x \leq 7 \]
   Simplifying, we get:
   \[ 4 - 5x \leq 7 \]

2. Subtract 4 from both sides:
   \[ 4 - 4 - 5x \leq 7 - 4 \]
   Simplifying, we get:
   \[ -5x \leq 3 \]

3. Divide both sides by -5 (and remember to reverse the inequality sign because we are dividing by a negative number):
   \[ x \geq \frac{3}{-5} \]
   Simplifying, we get:
   \[ x \geq -\frac{3}{5} \]

So, the solution to the inequality \(4 - 3x \leq 2x + 7\) is:
\[ x \geq -\frac{3}{5} \]

Expressed as an interval, the solution is:
\[ \left[ -\frac{3}{5}, \infty \right) \]

If you have a specific inequality in mind or any other type of problem, please provide the details so I can assist you accordingly.

Would you like more details or have any questions about this solution?

Here are some related questions you might find interesting:
1. What is the solution to \(5x - 3 \leq 7x + 4\)?
2. How do you solve \(2x + 5 \leq 4x - 3\) for \( x \)?
3. What is the solution to \(4x - 9 \geq 6x - 2\)?
4. How do you solve the compound inequality \(1 < 2x + 3 \leq 7\)?
5. What are the solutions to \(5x + 2 < 3x + 10\)?
6. How do you find the interval notation for \(2x - 4 > x + 6\)?
7. What is the solution to \(3x - 5 \leq 4x + 1\)?
8. How do you solve the inequality \(7 - 2x \geq 3x + 5\)?

**Tip:** When solving inequalities, ensure each step is correctly simplifying the terms to avoid mistakes in reversing inequality signs or misinterpreting results.

Learn how to find all real numbers x that satisfy the inequality 4 - 3x ≤ 2x + 7 with a step-by-step solution. This problem covers solving linear inequalities and includes detailed algebraic steps to determine the interval of solutions. Suitable for students in Grades 7-9.

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