Question

QUESTION:Below are a series of statements regarding the number line graph shown below. Which statement(s) are FALSE? Select all that apply.I: Number Line A represents the inequality x > 6.II: Number Line B represents the solution to the inequality -4x - 9 < -29.III: Number Line C includes the integer -5 as a possible solution.IV: Number Line D represents the inequality x ≤ 5.ANSWERS:A. I onlyB. I and IVC. None of the combinations of statements above are false.D. II, III and IVE. IV only

Answer 1

Given the statements and the number lines shown in the picture, you need to check each statement in order to determine which are false:

1. According to Statement I, the Number Line represents the inequality:

`x>6`

In Number Line A you can observe a closed circle over the number 6.

By definition, closed circles are used when you have to represent inequalities that have one of these symbols:

`\leq\text{ or }\ge`

Therefore, you can conclude that this statement is false.

2. According to Statement II, Number Line B represents the solution to the inequality:

`-4x-9<-29`

Then, you need to solve it to check it:

`\begin{gathered} -4x<-29+9 \\ \\ -4x<-20 \\ \\ x>(-20)/(-4) \\ \\ x>5 \end{gathered}`

(Notice that since you divided both sides by a negative number, the direction of the inequality symbol changed).

The solution indicates that the Number Line must contain an open circle over the number 5, and the line must go from the circle to the right.

Therefore, since Number Line B satisfies that description, you can conclude that Statement II is true.

3. According to Statement III, Number Line C includes the integer -5 as a possible solution.

Notice that the red line goes from the opened circle to the left. That is the direction of the numbers that make that inequality true. Based on the number line, the solution is:

`x<6`

Since:

`-5<6`

You can determine that the statement is true.

4. Statement IV indicates that Number Line D represents the inequality:

`x\le5`

Since the number line shows that the red line goes from the closed circle to the left, you can conclude that the statement is true, because the symbol of the inequality is:

`\leq`

Hence, the answer is: Option A.