https://file.aiquickdraw.com/mathbot/file/1728524101600hhwljt4m.jpg

To solve the inequality \( 7x > -42 \) and represent it on the number line, let's go through the steps.

### Step 1: Solve for \( x \)
The inequality given is:
\[
7x > -42
\]
To isolate \( x \), divide both sides by 7:
\[
x > -6
\]

### Step 2: Write the Solution in Inequality Notation
The inequality notation for this solution is:
\[
x > -6
\]

### Step 3: Graph the Solution on the Number Line
To graph \( x > -6 \) on the number line:
1. Locate -6 on the number line.
2. Draw an open circle around -6 to indicate that -6 is not included in the solution (since it’s a strict inequality, \( > \) not \( \geq \)).
3. Shade the region to the right of -6, showing all values greater than -6.

Would you like more detailed steps, or do you have any specific questions about this problem?

---

Here are some related questions to expand your understanding:
1. How would the solution change if the inequality were \( 7x \geq -42 \)?
2. What steps would be needed if the inequality were \( -7x > -42 \)?
3. How would you graph \( x \leq -6 \) on the number line?
4. What would happen to the inequality direction if you divided by a negative number?
5. Can you solve and graph \( 5x + 2 > 12 \)?

**Tip:** When solving inequalities, remember that dividing or multiplying by a negative number reverses the inequality sign.

Solve for x and graph the solution on the number line below: 7x > -42.

Learn how to solve the inequality 7x > -42 and graph the solution on a number line. This problem introduces key algebraic concepts such as solving one-step inequalities and representing them graphically. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation