For a given input value m, the function g outputs a value n to satisfy the following equation. -2m-5n=7m-3n Write a formula for g(m) in terms of m. g(m)=

Isolate n in equation: First, we need to isolate n on one side of the equation to find a formula for g(m) in terms of m. We start with the given equation: -2m - 5n = 7m - 3nCombine like terms: Combine like terms by adding 5n to both sides and adding 2m to both sides to get all the m terms on one side and all the n terms on the other side: -2m + 2m - 5n + 5n = 7m + 2m - 3n + 5n This simplifies to: 0m = 9m + 2nSubtract 9m to isolate n: Now, subtract 9m from both sides to isolate the terms with n: 0m - 9m = 9m - 9m + 2n This simplifies to: -9m = 2nDivide both sides by 2: To solve for n, divide both sides by 2: n = -9m / 2Formula for g(m): Now we have n in terms of m, which means we have found the formula for g(m): g(m) = -9m / 2

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

-2m-5n=7m-3n
Write a formula for
g(m) in terms of
m.

g(m)=

For a given input value $m$ , the function $g$ outputs a value $n$ to satisfy the following equation. $\newline$ $-2m-5n=7m-3n$ $\newline$ Write a formula for $g(m)$ in terms of $m$ . $\newline$ $g(m)=$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

m

, the function

g

outputs a value

n

to satisfy the following equation.

\newline

-2m-5n=7m-3n

\newline

Write a formula for

g(m)

in terms of

m

\newline

g(m)=

Isolate $n$ in equation: First, we need to isolate $n$ on one side of the equation to find a formula for $g(m)$ in terms of $m$ . We start with the given equation: $\newline$ $-2$ m - $5$ n = $7$ m - $3$ n
Combine like terms: Combine like terms by adding $5n$ to both sides and adding $2m$ to both sides to get all the $m$ terms on one side and all the $n$ terms on the other side: $\newline$ $-2m + 2m - 5n + 5n = 7m + 2m - 3n + 5n$ $\newline$ This simplifies to: $\newline$ $0m = 9m + 2n$
Subtract $9m$ to isolate $n$ : Now, subtract $9m$ from both sides to isolate the terms with $n$ : $0m - 9m = 9m - 9m + 2n$ This simplifies to: $-9m = 2n$
Divide both sides by $2$ : To solve for $n$ , divide both sides by $2$ : $\newline$ $n = \frac{-9m}{2}$
Formula for g(m): Now we have $n$ in terms of $m$ , which means we have found the formula for $g(m)$ : $\newline$ $g(m) = -\frac{9m}{2}$