Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Let

x ----> the cost of the concert ticket

we know that

The total cost to be no more than $4 Above  $80

so

$5x\leq 80+4$

Solve for x

$x\leq \ 16.80$

The total cost to be no more than $4  below $80

so

$5x\geq 80-4$

Solve for x

$5x\geq 76$

$x\geq \ 15.2$

therefore

The inequality that represent this problem is

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

Verify

First solution (positive case)

$+(5x-80)\le 4$

$5x\le 80+4$

Solve for x

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

Second solution (negative case)

$-(5x-80)\le 4$

Multiply by -1 both sides

$(5x-80)\ge -4$

$5x\geq 80-4$

Solve for x

$5x\geq 76$

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

Remember that

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

Because is a absolute value