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$3(2x-6)-11=4(x-3)+6$
If $x$ is the solution to the equation above, what is the value of $x-3$?
Difficulty: Medium
A:
$\frac{23}{2}$
B:
$\frac{17}{2}$
C:
$\frac{15}{2}$
D:
$-\frac{15}{2}$
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $\$5$. Assuming gasoline costs $\$4$ per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?
Difficulty: Hard
A:
$\frac{25}{4}m=95$
B:
$\frac{25}{4}m=5$
C:
$\frac{4}{25}m=95$
D:
$\frac{4}{25}m=5$
A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let $d$ represent the number of containers of detergent, and let $s$ represent the number of containers of fabric softener, where $d$ and $s$ are nonnegative integers. Which of the following systems of inequalities best represents this situation?
Difficulty: Hard
A:
$7.35d+6.2s\leq 300 \\ d\geq 2s$
B:
$7.35d+6.2s\leq 300 \\ 2d\geq s$
C:
$14.7d+6.2s\leq 300 \\ d\geq 2s$
D:
$14.7d+6.2s\leq 300 \\ 2d\geq s$
The function $g$ is defined by $g(x)=-x+8$. What is the value of $g(0)$?
Difficulty: Easy
A:
$-8$
B:
$0$
C:
$4$
D:
$8$
$y\leq x$
$y\leq-x$
Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?
Difficulty: Medium
A:
$(1,0)$
B:
$(-1,0)$
C:
$(0,1)$
D:
$(0,-1)$
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