x−5<−11 or x−1≥−5  Solve the inequality for x

To solve the compound inequality \( x - 5 < -11 \) or \( x - 1 \geq -5 \), we will solve each part separately.

### 1. Solve \( x - 5 < -11 \):
\[
x - 5 < -11
\]
Add 5 to both sides:
\[
x < -11 + 5
\]
\[
x < -6
\]

### 2. Solve \( x - 1 \geq -5 \):
\[
x - 1 \geq -5
\]
Add 1 to both sides:
\[
x \geq -5 + 1
\]
\[
x \geq -4
\]

### 3. Combine the solutions:
The solution to the compound inequality is the union of the two individual solutions:
\[
x < -6 \quad \text{or} \quad x \geq -4
\]

So, the solution for \( x \) is \( x < -6 \) or \( x \geq -4 \).

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

Here are 5 related questions for further practice:

1. Solve the inequality: \( 2x - 3 < 5 \) or \( x + 4 \geq 9 \).
2. Solve the compound inequality: \( 3x + 2 > 8 \) and \( 5x - 7 \leq 13 \).
3. Solve the inequality: \( x - 2 < 4 \) or \( 2x + 1 > 7 \).
4. Solve the compound inequality: \( 4x - 3 \leq 1 \) or \( x + 2 > 10 \).
5. Solve the inequality: \( 2x + 5 > 9 \) or \( x - 6 \leq -2 \).

**Tip:** When solving compound inequalities, remember that "or" means you combine the solutions from each part, while "and" means you take the intersection of the solutions.

Solve the inequality for x: x - 5 < -11 or x - 1 ≥ -5

Learn how to solve the linear inequalities x - 5 < -11 or x - 1 ≥ -5 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving basic linear inequalities and understanding properties of inequalities. Suitable for students in Grades 7-8.

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