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Anuta_ua [19.1K]

2 years 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:

kumpel [21]2 years ago

8 0

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

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

<u><em>Verify</em></u>

<em>First solution (positive case</em>)

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

$5x\le 80+4$

Solve for x

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

<em>Second solution (negative case)</em>

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

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

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