For a given input value u, the function h outputs a value v to satisfy the following equation. 4u+8v=-3u+2v Write a formula for h(u) in terms of u. h(u)=

Combine like terms: Combine like terms by moving all terms involving u to one side of the equation and all terms involving v to the other side. 4u + 8v = -3u + 2v Add 3u to both sides and subtract 2v from both sides to isolate terms with u and v. 4u + 3u + 8v - 2v = -3u + 3u + 2v - 2v 7u + 6v = 0Isolate terms with u and v: Solve for v in terms of u. To isolate v, divide both sides of the equation by 6. v = -7u/6Solve for v in terms of u: Write the function h(u) in terms of u. Since h outputs a value v for a given input u, and we have found that v = -7u/6, the function h(u) is: h(u) = -7u/6

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For a given input value
u, the function
h outputs a value
v to satisfy the following equation.

4u+8v=-3u+2v
Write a formula for
h(u) in terms of
u.

h(u)=

For a given input value $u$ , the function $h$ outputs a value $v$ to satisfy the following equation. $\newline$ $4u + 8v = -3u + 2v$ $\newline$ Write a formula for $h(u)$ in terms of $u$ . $\newline$ $h(u) =$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

u

, the function

h

outputs a value

v

to satisfy the following equation.

\newline

4u + 8v = -3u + 2v

\newline

Write a formula for

h(u)

in terms of

u

\newline

h(u) =

Combine like terms: Combine like terms by moving all terms involving $u$ to one side of the equation and all terms involving $v$ to the other side. $\newline$ $4$ u + $8$ v = $-3$ u + $2$ v $\newline$ Add $3$ u to both sides and subtract $2$ v from both sides to isolate terms with $u$ and $v$ . $\newline$ $4$ u + $3$ u + $8$ v - $2$ v = $-3$ u + $3$ u + $2$ v - $2$ v $\newline$ $7$ u + $6$ v = $0$
Isolate terms with $u$ and $v$ : Solve for $v$ in terms of $u$ . $\newline$ To isolate $v$ , divide both sides of the equation by $6$ . $\newline$ $v = \frac{-7u}{6}$
Solve for $v$ in terms of $u$ : Write the function $h(u)$ in terms of $u$ . $\newline$ Since $h$ outputs a value $v$ for a given input $u$ , and we have found that $v = -\frac{$ $7$ }{ $6$ }u, the function $h(u)$ is: $\newline$ $h(u) = -\frac{$ $7$ }{ $6$ }u