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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 12$ , find $y$ when $x = 4$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Write and solve inverse variation equations

Full solution

Q. Assume that

y

varies inversely with

x

. If

y = 2

when

x = 12

, find

y

when

x = 4

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

_____

Identify general form: Given that $y$ varies inversely with $x$ . Identify the general form of inverse variation. In inverse variation, variables change in opposite directions. Inverse variation: $y = \frac{k}{x}$
Substitute values in equation: We know that $y = 2$ when $x = 12$ . Choose the equation after substituting the values in $y = \frac{k}{x}$ . Substitute $12$ for $x$ and $2$ for $y$ in $y = \frac{k}{x}$ . $2 = \frac{k}{12}$
Solve for k: We found: $\newline$ $2 = \frac{k}{12}$ $\newline$ Solve the equation to find the value of k. $\newline$ To isolate k, multiply both sides by $12$ . $\newline$ $2 \times 12 = \left(\frac{k}{12}\right) \times 12$ $\newline$ $24 = k$
Write inverse variation equation: We have: $\newline$ $k = 24$ $\newline$ Write the inverse variation equation in the form of $y = \frac{k}{x}$ . $\newline$ Substitute $k = 24$ in $y = \frac{k}{x}$ . $\newline$ $y = \frac{24}{x}$
Find $y$ for $x=4$ : Inverse variation equation: $\newline$ $y = \frac{24}{x}$ $\newline$ Find $y$ when $x = 4$ . $\newline$ Substitute $4$ for $x$ in $y = \frac{24}{x}$ . $\newline$ $y = \frac{24}{4}$ $\newline$ $y = 6$

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