Expressions, Equations, and Relationships>Writing One-Variable Equations and Inequalities with Variables on Both Sides(TEKS.Math.8.8.A)
Help Questions
Texas 8th Grade Math › Expressions, Equations, and Relationships>Writing One-Variable Equations and Inequalities with Variables on Both Sides(TEKS.Math.8.8.A)
Two cell plans charge a monthly fee plus a cost per gigabyte of data. Plan A charges a monthly fee of 15 dollars plus 4.50 dollars per GB. Plan B charges a monthly fee of 9 dollars plus 6 dollars per GB. Let $x$ be the number of gigabytes used in a month.
What equation shows when the two monthly costs are equal?
$15 + 4.5x = 9 + 6x$
$15 + 4.5 = 9 + 6x$
$4.5x = 9 + 6x$
$15 + 4.5x \le 9 + 6x$
Explanation
Equal costs means set Plan A's expression equal to Plan B's: $15 + 4.5x = 9 + 6x$. Choice B drops the variable on 4.5, C omits the monthly fee for Plan A, and D is an inequality instead of an equation.
Two gym membership options each have a one-time joining fee and a monthly cost. Plan 1 charges a 25 dollar joining fee plus 12 dollars per month. Plan 2 charges a 10 dollar joining fee plus 15 dollars per month. Let $x$ be the number of months.
Which equation represents the month count when the total costs are the same?
$25 + 12 = 10 + 15x$
$12x = 10 + 15x$
$25 + 12x = 10 + 15x$
$25 + 12x \ge 10 + 15x$
Explanation
Equal total cost means set Plan 1's total equal to Plan 2's: $25 + 12x = 10 + 15x$. A drops the variable on 12, B omits the joining fee for Plan 1, and D uses an inequality instead of an equation.
A moving truck company charges a daily fee plus a cost per mile. Company A charges 40 dollars per day plus 0.75 dollars per mile. Company B charges 25 dollars per day plus 1.10 dollars per mile. Let $x$ be the number of miles driven in a day.
What equation shows when both companies cost the same amount for a day?
$40x + 0.75 = 25 + 1.10x$
$40 + 0.75x \ge 25 + 1.10x$
$40 + 0.75x = 1.10x - 25$
$40 + 0.75x = 25 + 1.10x$
Explanation
Set the two cost expressions equal: $40 + 0.75x = 25 + 1.10x$. A swaps where $x$ goes (multiplying 40 by $x$), B uses an inequality, and C moves the daily fee 25 to the wrong side with a sign change.
Two movie-watching options: Plan R charges a 5 dollar access fee plus 3.50 dollars per movie. Plan S charges a 12 dollar monthly fee plus 2 dollars per movie. Let $x$ be the number of movies watched in a month.
Which equation represents this situation when the total monthly costs are equal?
$5 + 3.50 = 12 + 2x$
$5 + 3.50x = 12 + 2x$
$5x + 3.50 = 12 + 2x$
$5 + 3.50x = 12x + 2$
Explanation
Equal costs means Plan R's total equals Plan S's total: $5 + 3.50x = 12 + 2x$. A drops the variable on 3.50, C multiplies the fee by $x$, and D misplaces the $x$ with the 12 instead of the 2.
Two printers charge a setup fee plus a price per T-shirt for a school order. Printer A charges a 30 dollar setup fee plus 8.50 dollars per shirt. Printer B charges a 12 dollar setup fee plus 9.25 dollars per shirt. Let $x$ be the number of shirts.
What equation shows when the two printers cost the same?
$30 + 8.5x = 12 + 9.25x$
$30 + 8.5x = 12x + 9.25$
$30x + 8.5 = 12 + 9.25x$
$30 + 8.5x \le 12 + 9.25x$
Explanation
Set the total cost expressions equal: $30 + 8.5x = 12 + 9.25x$. B swaps the setup fee and per-shirt roles on B's side, C multiplies the setup fee by $x$, and D incorrectly uses an inequality.