An accountant is working on projections for his next assignment and finds that the cost to the company, C, can be expressed as |C-20,000|<4,000.
a) solve for the projected cost by writing a compund inequality; then write it as an absolute value inequality.
|C-20000| < 4000
means
+(C-20000) < 4000 and -(C-20000) < 4000
C - 20000 < 4000 and -C +20000 < 4000
C < 24000 and c > 20000-400
C < 24000 and C > 16000
Compound inequality
16000 < C < 24000
|C-20,000|<4,000
is already an absolute value inequality.
m=-6
To solve the compound inequality |C-20,000| < 4,000, we first need to understand what the absolute value inequality means.
The inequality |C-20,000| < 4,000 states that the difference between C and 20,000 falls within the range of -4,000 to 4,000. This means that the value of C should be within 4,000 units below and 4,000 units above 20,000.
To express this as a compound inequality, we can break it down into two inequalities:
-4,000 < C - 20,000 < 4,000
Now, let's solve each inequality separately:
First inequality:
-4,000 < C - 20,000
Add 20,000 to both sides:
20,000 - 4,000 < C - 20,000 + 20,000
16,000 < C
Second inequality:
C - 20,000 < 4,000
Add 20,000 to both sides:
C - 20,000 + 20,000 < 4,000 + 20,000
C < 24,000
Therefore, the projected cost C falls between 16,000 and 24,000 (exclusive on the 16,000 side and inclusive on the 24,000 side).
To write the compound inequality as an absolute value inequality, we can combine the two inequalities:
16,000 < C and C < 24,000
Combining both inequalities, we can express it as:
|C - 20,000| < 4,000
This represents that the difference between C and 20,000 is less than 4,000.