Let's analyze the situation presented:
Vera claimed that the solution set on the number line represents the inequality [tex]\(-78.9999 \geq x\)[/tex]. To determine the error Vera made, we need to understand the correct representation of this inequality.
1. Identify the Inequality Direction:
The inequality [tex]\(-78.9999 \geq x\)[/tex] can be written with the variable [tex]\(x\)[/tex] on the left-hand side for easier interpretation. This becomes:
[tex]\[
x \leq -78.9999
\][/tex]
This inequality states that [tex]\(x\)[/tex] is less than or equal to [tex]\(-78.9999\)[/tex].
2. Check the Correct Relation Symbol:
Now, let's see if this correctly matches Vera's original version. Vera wrote [tex]\(-78.9999 \geq x\)[/tex]. The correct form as interpreted is:
[tex]\[
x \leq -78.9999
\][/tex]
Comparing this to Vera's claim, the inequality symbol [tex]\( \geq \)[/tex] (greater than or equal to) should indeed represent the opposite direction (i.e., less than or equal to).
3. Determine the Error Made:
Analyzing what Vera did:
- Vera wrote the variable [tex]\(x\)[/tex] on the right side: This part is correct; variables can be on either side.
- The relation symbol used: Here is the evaluation point. [tex]\(\geq\)[/tex] does not correctly represent the intended ray direction on the number line. The correct relation should be [tex]\(\leq\)[/tex].
- Inequality Inclusion: Vera's representation does not change the value [tex]\(-78.9999\)[/tex], thus this part is accurate.
- Number Used: Vera used [tex]\(-78.9999\)[/tex] correctly according to the initial information provided.
Thus, the error lies in the incorrect relation symbol. Vera should have used the symbol representing [tex]\(x\)[/tex] being less than or equal to [tex]\(-78.9999\)[/tex], which corresponds to:
Vera wrote a relation symbol that does not represent the direction of the ray.
So, the error that Vera made is:
Vera wrote a relation symbol that does not represent the direction of the ray.
The correct answer is [tex]\(2\)[/tex].
