few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Your response, in json format:
{
  "explanation": "This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
problem_activity: Problem 1
Consider the three situations shown below.
$${|x|=5}$$
$${|x|<5}$$
$${|x|>5}$$
For each situation, let
$${{f(x)}=|x|}$$
and
$${{g(x)}=5}$$
. Graph each relationship between
$${f(x)}$$
and
$${g(x)}$$
in the coordinate plane and then use each graph to determine the solution to each situation.
Problem 2
Solve each absolute value inequality algebraically and verify the solution graphically.
a.
$${\left|x-{1\over2}\right|<3}$$
b.
$${\left|2x\right|>{7\over2}}$$
c.
$${\left|{1\over3}x\right|-4<-1}$$


correct_option_index: 1