Question

plot the inequality on the number line.
-6 < x ≤ 5

choose the proper tool with the correct endpoints then click and drag the endpoints to the correct location.
notice the trash can is available if an error is made.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
tools

Explanation:

Step1: Analyze the inequality

The inequality is \(-6 < x \leq 5\). This means \(x\) is greater than \(-6\) (not including \(-6\)) and less than or equal to \(5\) (including \(5\)).

Step2: Choose the correct tool

For the left - hand side (\(x > - 6\)), we use an open circle (since \(-6\) is not included in the solution set) at \(-6\). For the right - hand side (\(x\leq5\)), we use a closed circle (since \(5\) is included in the solution set) at \(5\). Then we draw a line segment connecting the open circle at \(-6\) and the closed circle at \(5\) to represent all the values of \(x\) that satisfy the inequality.

Step3: Place the endpoints on the number line

• Locate \(-6\) on the number line. Since \(x > - 6\), we place an open circle at \(-6\).
• Locate \(5\) on the number line. Since \(x\leq5\), we place a closed circle at \(5\).
• Then draw a line from the open circle at \(-6\) to the closed circle at \(5\) to show the interval of values that \(x\) can take.

Answer:

To plot \(-6 < x\leq5\) on the number line:

1. Place an open circle at \(-6\) (because \(x\) is greater than, not equal to, \(-6\)).
2. Place a closed circle at \(5\) (because \(x\) is less than or equal to \(5\)).
3. Draw a line segment connecting the open circle at \(-6\) and the closed circle at \(5\) to represent the solution set.