To determine whether a starting salary [tex]\( x \)[/tex] falls within the given range, we need to express the condition that [tex]\( x \)[/tex] can vary by less than \[tex]$1,300 from the average salary of \$[/tex]39,800. This can be translated into an absolute value inequality.
Given:
- Average starting salary: \[tex]$39,800
- Variation: Less than \$[/tex]1,300
The inequality representing this condition is:
[tex]\[ |x - 39,800| < 1,300 \][/tex]
Hence, the correct choice for the inequality is:
C. [tex]\( |x - 39,800| < 1,300 \)[/tex]
To find the range of starting salaries, we will solve the inequality:
[tex]\[ |x - 39,800| < 1,300 \][/tex]
This inequality can be broken down into two parts:
[tex]\[ -1,300 < x - 39,800 < 1,300 \][/tex]
Now, we solve for [tex]\( x \)[/tex] in these two parts:
1. [tex]\( -1,300 < x - 39,800 \)[/tex]
Adding 39,800 to both sides:
[tex]\[ -1,300 + 39,800 < x \][/tex]
[tex]\[ 38,500 < x \][/tex]
2. [tex]\( x - 39,800 < 1,300 \)[/tex]
Adding 39,800 to both sides:
[tex]\[ x < 1,300 + 39,800 \][/tex]
[tex]\[ x < 41,100 \][/tex]
Combining these two results, the range of starting salaries is:
[tex]\[ 38,500 < x < 41,100 \][/tex]
So, the range of starting salaries at the company is from \[tex]$38,500 to \$[/tex]41,100.
Therefore, the correct choice is indeed:
C. [tex]\( |x - 39,800| < 1,300 \)[/tex] The range of salaries is from \[tex]$38,500 to \$[/tex]41,100.
