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

-2u+6v=9
Write a formula for
h(v) in terms of
v.

h(v)=◻

For a given input value $v$ , the function $h$ outputs a value $u$ to satisfy the following equation. $\newline$ $-2u+6v=9$ $\newline$ Write a formula for $h(v)$ in terms of $v$ . $\newline$ $h(v)=\square$

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Find the inverse of a linear function

Full solution

Q. For a given input value

v

, the function

h

outputs a value

u

to satisfy the following equation.

\newline

-2u+6v=9

\newline

Write a formula for

h(v)

in terms of

v

.

\newline

h(v)=\square

Isolate terms with $u$ : To find the formula for $h(v)$ , we need to solve the equation $-2$ u + $6$ v = $9$ for $u$ in terms of $v$ .
Add $2u$ to both sides: First, we add $2u$ to both sides of the equation to isolate the terms with $u$ on one side. $\newline$ $-2u + 6v + 2u = 9 + 2u$ $\newline$ This simplifies to: $\newline$ $6v = 9 + 2u$
Subtract $9$ from both sides: Next, we subtract $9$ from both sides to get the terms with $v$ on one side. $6v - 9 = 9 + 2u - 9$ This simplifies to: $6v - 9 = 2u$
Divide both sides by $2$ : Now, we divide both sides by $2$ to solve for $u$ .
$\frac{6v - 9}{2} = \frac{2u}{2}$
This simplifies to:
$u = \frac{6v - 9}{2}$
Write $h(v)$ in terms of $v$ : Finally, we write the function $h(v)$ in terms of $v$ using the expression we found for $u$ . $h(v) = \frac{6v - 9}{2}$

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