To solve the compound inequality \( 4x - 2 < 2 \) and \( 4x + 6 \geq -10 \), let's address each inequality separately.

### First Inequality: \( 4x - 2 < 2 \)

1. Add 2 to both sides:
   \[
   4x < 4
   \]
2. Divide both sides by 4:
   \[
   x < 1
   \]

### Second Inequality: \( 4x + 6 \geq -10 \)

1. Subtract 6 from both sides:
   \[
   4x \geq -16
   \]
2. Divide both sides by 4:
   \[
   x \geq -4
   \]

### Combine the Results

Now, combine the two results:
\[
-4 \leq x < 1
\]
This means \( x \) can take any value from \(-4\) to \(1\), including \(-4\) but not including \(1\).

### Do you want details or have any questions? 

Here are five related questions:

1. How would the solution change if the second inequality was \( 4x + 6 > -10 \)?
2. Can you graph the solution set for this compound inequality on a number line?
3. What would be the solution if the inequalities were \( 4x - 2 > 2 \) and \( 4x + 6 \leq -10 \)?
4. How do you solve inequalities involving fractions or decimals?
5. What is the difference between solving inequalities and solving equations?

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

Learn how to solve the compound inequality 4x - 2 < 2 and 4x + 6 ≥ -10 step-by-step. This problem covers key algebraic concepts involving inequalities. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation