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

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

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