Question

Math

Posted 5 months ago

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

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Given the equation from asksia-ll calculation list: $-2u + 6v = 9$

step 2

To solve for $u$ in terms of $v$, isolate $u$ on one side of the equation

step 3

Add $2u$ to both sides of the equation to get $6v = 9 + 2u$

step 4

Subtract $9$ from both sides to get $6v - 9 = 2u$

step 5

Divide both sides by $2$ to solve for $u$: $u = 3v - \frac{9}{2}$

step 6

The function $h(v)$ that outputs $u$ is therefore $h(v) = 3v - \frac{9}{2}$

Answer

$h(v) = 3v - \frac{9}{2}$

Key Concept

Solving a linear equation for a variable

Explanation

To find $h(v)$, we isolate $u$ in the given equation and express it as a function of $v$. The steps involve rearranging the equation and solving for $u$.

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