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For a given input value
n, the function
g outputs a value
m to satisfy the following equation.

3m-5n=11
Write a formula for
g(n) in terms of
n.

g(n)=◻

For a given input value $n$ , the function $g$ outputs a value $m$ to satisfy the following equation. $\newline$ $3m-5n=11$ $\newline$ Write a formula for $g(n)$ in terms of $n$ . $\newline$ $g(n)=\square$

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Find the inverse of a linear function

Full solution

Q. For a given input value

n

, the function

g

outputs a value

m

to satisfy the following equation.

\newline

3m-5n=11

\newline

Write a formula for

g(n)

in terms of

n

.

\newline

g(n)=\square

Isolate m in equation: Isolate m in the equation $3m - 5n = 11$ . $\newline$ To do this, we will add $5n$ to both sides of the equation to get $3m$ on one side. $\newline$ $3m - 5n + 5n = 11 + 5n$ $\newline$ This simplifies to: $\newline$ $3m = 11 + 5n$
Divide both sides by $3$ : Divide both sides of the equation by $3$ to solve for m. $\newline$ $\frac{3m}{3} = \frac{11 + 5n}{3}$ $\newline$ This simplifies to: $\newline$ $m = \frac{11 + 5n}{3}$
Write function $g(n)$ in terms of $n$ : Write the function $g(n)$ in terms of $n$ using the expression for $m$ . $\newline$ Since $m$ is the output of the function $g$ for the input $n$ , we can write: $\newline$ $g(n) = \frac{11 + 5n}{3}$

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