Answer:
Option C [tex]\left|80-5x\right|\le 4[/tex]
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
[tex]5x\leq 80+4[/tex]
Solve for x
[tex]x\leq \$16.80[/tex]
The total cost to be no more than $4 below $80
so
[tex]5x\geq 80-4[/tex]
Solve for x
[tex]5x\geq 76[/tex]
[tex]x\geq \$15.2[/tex]
therefore
The inequality that represent this problem is
[tex]\left|5x-80\right|\le 4[/tex]
Verify
First solution (positive case)
[tex]+(5x-80)\le 4[/tex]
[tex]5x\le 80+4[/tex]
Solve for x
[tex]x\leq \$16.80[/tex] ----> is ok
Second solution (negative case)
[tex]-(5x-80)\le 4[/tex]
Multiply by -1 both sides
[tex](5x-80)\ge -4[/tex]
[tex]5x\geq 80-4[/tex]
Solve for x
[tex]5x\geq 76[/tex]
[tex]x\geq \$15.2[/tex] ---> is ok
Remember that
[tex]\left|5x-80\right|\le 4[/tex] is equivalent to [tex]\left|80-5x\right|\le 4[/tex]
Because is a absolute value
