Question

solve for x and graph the solution on the number line below.
7x > -42
answer attempt 1 out of 10
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line

Explanation:

Step1: Divide both sides by 7

To solve for \( x \) in the inequality \( 7x > -42 \), we divide both sides by 7 (since 7 is positive, the inequality sign remains the same). So we have \( \frac{7x}{7} > \frac{-42}{7} \).

Step2: Simplify both sides

Simplifying the left side gives \( x \), and simplifying the right side gives \( -6 \). So the solution is \( x > -6 \).

Answer:

Inequality Notation: \( x > -6 \)
For the number line: We would draw an open circle at -6 (since the inequality is \( > \), not \( \geq \)) and shade the line to the right of -6 to represent all numbers greater than -6.