x-2≤2 and x+1≥3 whats the solution set

To solve the compound inequality \(x - 2 \leq 2\) and \(x + 1 \geq 3\), we will solve each inequality separately and then find the intersection (overlap) of their solution sets.

### Step-by-step Solution:

1. **Solve the first inequality:**

   \[
   x - 2 \leq 2
   \]

   Add 2 to both sides:

   \[
   x \leq 4
   \]

2. **Solve the second inequality:**

   \[
   x + 1 \geq 3
   \]

   Subtract 1 from both sides:

   \[
   x \geq 2
   \]

3. **Find the intersection of the solution sets:**

   - The solution set for \(x \leq 4\) is all \(x\) values less than or equal to 4.
   - The solution set for \(x \geq 2\) is all \(x\) values greater than or equal to 2.

   The intersection of these two sets is the range of \(x\) values that satisfy both conditions.

### Solution Set:

\[
2 \leq x \leq 4
\]

### In Interval Notation:

\[
[2, 4]
\]

This means the solution set includes all \(x\) values from 2 to 4, inclusive.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. Solve the compound inequality \(x + 3 > 5\) and \(x - 4 < 0\).
2. What is the solution set for \(3x + 2 \leq 5x - 6\) and \(x - 1 > 4\)?
3. Solve the inequality \(2x - 7 \geq 5 - x\).
4. Find the solution set for the compound inequality \(4x - 1 < 15\) and \(x + 2 > 0\).
5. Determine the interval notation for the solution set of \(x - 5 \leq -3\) or \(x + 2 \geq 6\).

**Tip:** When solving compound inequalities, always solve each inequality separately before finding the intersection or union of their solutions.

Learn how to solve the compound inequalities x-2≤2 and x+1≥3 with a detailed step-by-step solution. This problem covers key concepts in inequalities and set intersections. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation