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12 days 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

1 answer:

Zina [3.9K]12 days 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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