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

Accepted Solution

Answer:Option C [tex]\left|80-5x\right|\le 4[/tex]Step-by-step explanation:Letx ----> the cost of the concert ticketwe know thatThe total cost to be no more than $4 Above  $80so[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 $80so[tex]5x\geq 80-4[/tex]Solve for x[tex]5x\geq 76[/tex][tex]x\geq \$15.2[/tex]thereforeThe inequality that represent this problem is[tex]\left|5x-80\right|\le 4[/tex]VerifyFirst 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 okSecond 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 okRemember 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