−34 ≤−4x−2 or −4x−2≤−46



We are given the compound inequality:

\[
-34 \leq -4x - 2 \quad \text{or} \quad -4x - 2 \leq -46
\]

Let's solve each inequality separately.

### Inequality 1: \(-34 \leq -4x - 2\)

1. Add 2 to both sides:
   \[
   -34 + 2 \leq -4x
   \]
   \[
   -32 \leq -4x
   \]

2. Divide both sides by \(-4\), remembering to flip the inequality sign since we are dividing by a negative number:
   \[
   \frac{-32}{-4} \geq x
   \]
   \[
   8 \geq x
   \]
   This simplifies to:
   \[
   x \leq 8
   \]

### Inequality 2: \(-4x - 2 \leq -46\)

1. Add 2 to both sides:
   \[
   -4x \leq -46 + 2
   \]
   \[
   -4x \leq -44
   \]

2. Divide both sides by \(-4\), again flipping the inequality:
   \[
   \frac{-4x}{-4} \geq \frac{-44}{-4}
   \]
   \[
   x \geq 11
   \]

### Final Answer:
The solution is the union of \(x \leq 8\) or \(x \geq 11\), meaning:

\[
x \in (-\infty, 8] \cup [11, \infty)
\]

Would you like any additional details on this solution?

### Related Questions:
1. How do you solve compound inequalities involving "and"?
2. What happens when dividing by negative numbers in inequalities?
3. How do you graph the solution of \(x \leq 8 \cup x \geq 11\)?
4. Can inequalities have infinite solutions?
5. What are the properties of inequalities under addition or subtraction?

**Tip:** Always remember to flip the inequality sign when dividing or multiplying both sides by a negative number.

Discover how to solve the compound inequality −34 ≤−4x−2 or −4x−2≤−46 with a detailed step-by-step explanation. Learn the key concepts of inequalities, flipping the inequality sign when dividing by negative numbers, and handling compound inequalities. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation