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Vlad1618
3 months ago
6

Jamie is buying 5 concert tickets, and he wants his total cost to be no more than $4 Above or below $80. Which inequality models

the cost x, in dollars, of a ticket? A.|5x+4|<80 B.|5x-4|<80 C.|80-5x|<4 D.|80+5x|<4
Mathematics
1 answer:
Zina [12.3K]3 months ago
8 0

Answer:

Option C \left|80-5x\right|\le 4

Step-by-step explanation:

Let

x ----> represent the price of a concert ticket

We know that

The total cost should not exceed $4 more than  $80

Therefore,

5x\leq 80+4

Solving for x gives:

x\leq \$16.80

The total cost should also not fall below $4 under $80

Hence,

5x\geq 80-4

Solve for x again:

5x\geq 76

x\geq \$15.2

This indicates that

The inequality representing this scenario is

\left|5x-80\right|\le 4

Verification

First solution (positive scenario)

+(5x-80)\le 4

5x\le 80+4

Resolve for x:

x\leq \$16.80 ----> is valid

Second solution (negative scenario)

-(5x-80)\le 4

Multiplying both sides by -1

(5x-80)\ge -4

5x\geq 80-4

Resolve for x:

5x\geq 76

x\geq \$15.2 ---> is valid

It is important to remember that

\left|5x-80\right|\le 4 is equivalent to \left|80-5x\right|\le 4

Due to the absolute value constraint.

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