Question

question
solve for x and graph the solution on the number line below.
3 > -x - 3 > -5
answer attempt 2 out of 2
inequality notation:
number line:
click and drag to plot line.
submit answer

Explanation:

Step1: Solve the left inequality

We have the compound inequality \(3 > -x - 3 > -5\). First, solve the left - hand side of the compound inequality \(3 > -x - 3\).
Add 3 to all parts of the inequality: \(3 + 3> -x - 3+ 3> -5 + 3\).
Simplify each part: \(6 > -x> - 2\).

Step2: Multiply by - 1 (reverse inequalities)

Multiply each part of the inequality \(6 > -x> - 2\) by - 1. When we multiply an inequality by a negative number, the direction of the inequality signs reverses.
So we get \(-6 < x < 2\).

Step3: Graph on the number line

To graph \( - 6 < x < 2\) on the number line:

• First, find the points - 6 and 2 on the number line.
• Since the inequality is strict ( \(<\), not \(\leq\) or \(\geq\) ), we use open circles at - 6 and 2.
• Then, we shade the region between - 6 and 2 on the number line.

Answer:

Inequality Notation: \(-6 < x < 2\)
For the number line: Open circles at - 6 and 2, and shade the region between them.