The manager of a band recommends that the band sell its CDs for $8.75. The band decides to sell the CD for p dollars.
A) Write an absolute value expression that tells how far the bands price is from the recommended price.
B) The band wants the price of its CD to be no more than $1.25 from the recommended price. Write an absolute value inequality that gives the range of the possible prices for the CD.
C) Solve the inequality. Write the solution as a compound inequality.
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A) To find the absolute value expression that measures how far the band's price is from the recommended price, we can subtract the recommended price from the band's price and take the absolute value.
Let x represent the band's price. The expression would be:
| x - 8.75 |
B) The absolute value inequality that gives the range of possible prices for the CD is:
| x - 8.75 | ≤ 1.25
C) To solve the absolute value inequality, we need to split it into two separate inequalities and solve them individually.
For the positive case:
x - 8.75 ≤ 1.25
x ≤ 10
For the negative case:
-(x - 8.75) ≤ 1.25
-x + 8.75 ≤ 1.25
-x ≤ -7.5
x ≥ 7.5
Combining both cases, the solution can be expressed as a compound inequality:
7.5 ≤ x ≤ 10