Question

Felix is buying 10 candles, and wants to spend no more than $5 above or below $80. Which inequality models the cost c, in dollars, Felix is willing to pay per candle?

A.

​|10c – 5| ≤ 80


B.

|80 – 10c| ≤ 5


C.

|80 + 10c| ≤ 5


D.

|10c + 5| ≤ 80

plz show work

Answer 1

B

Explanation:

We can go long way and solve each absolute value inequality and get out answer. Since he can go 5 above and below 80, our answer for cost, c, would be 75 and 85

One thing we need to know before solving absolute value equations is:

|ax+b| < c

means

ax+b < c & ax + b < -c

Now, we realize that if we have an equation in the form:

|ax + b| < D

we can say "ax" would be IN BETWEEN "D-b" and "D+b"

Looking at equation B, we can see that "-10c" would be between "5-80=-75" & "-5-80=-85"

Solving and showing:

80 - 10c ≤ 5

-10c ≤ -75

10c ≥ 75 [[ works]]

and

80 - 10c ≤ -5

-10c ≤ -85

10c ≥ 85

Hence, between 75 and 85.

Equation B is right.