https://file.aiquickdraw.com/mathbot/file/17290063636180rxgg1m8.jpg

The problem consists of two inequalities:

1. \( 42 < -4x + 2 \)
2. \( -38 \geq -4x + 2 \)

### Solving the first inequality:
\[
42 < -4x + 2
\]
Subtract 2 from both sides:
\[
42 - 2 < -4x
\]
\[
40 < -4x
\]
Now, divide both sides by -4, and remember to reverse the inequality sign when dividing by a negative number:
\[
\frac{40}{-4} > x
\]
\[
-10 > x
\]
Or equivalently:
\[
x < -10
\]

### Solving the second inequality:
\[
-38 \geq -4x + 2
\]
Subtract 2 from both sides:
\[
-38 - 2 \geq -4x
\]
\[
-40 \geq -4x
\]
Now divide both sides by -4, again reversing the inequality:
\[
\frac{-40}{-4} \leq x
\]
\[
10 \leq x
\]

### Combining the results:
We have:
\[
x < -10 \quad \text{or} \quad x \geq 10
\]

Thus, the solution is \( x < -10 \) or \( x \geq 10 \).

### Graphing the solution on a number line:
- Draw an open circle at \( x = -10 \) (because it is a strict inequality \( < \)).
- Shade to the left of \( -10 \) (since \( x < -10 \)).
- Draw a closed circle at \( x = 10 \) (since \( x \geq 10 \)).
- Shade to the right of \( 10 \).

Would you like a detailed graph or further explanation on this? 

Here are 5 relative questions:
1. How do you handle inequalities involving multiplication or division by a negative number?
2. Can you combine inequalities into a single inequality when using "or" or "and"?
3. How do strict inequalities differ from non-strict ones in graphing?
4. What are the implications of no solution in inequalities?
5. How can we check if our solution is correct?

**Tip:** Always remember to reverse the inequality when multiplying or dividing by a negative number!

Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank. 42 < -4x + 2 or -38 ≥ -4x + 2

Learn how to solve the compound inequalities 42 < -4x + 2 or -38 ≥ -4x + 2 with step-by-step solutions. Understand key algebraic concepts like solving inequalities and graphing them on a number line. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation