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 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 v on one side and terms with u on the other side. 4u + 3u + 8v - 2v = -3u + 3u + 2v - 2v 7u + 6v = 0Isolate terms with v and u: 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 v is the output of the function h for the input u, we can write h(u) = v. Therefore, h(u) = -7u/6

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $u$ . $\newline$ $h(u)=\square$

View step-by-step help

Home

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)=\square

Combine like terms: Combine like terms by moving all terms involving $u$ to one side and all terms involving $v$ to the other side. $\newline$ $4u + 8v = -3u + 2v$ $\newline$ Add $3u$ to both sides and subtract $2v$ from both sides to isolate terms with $v$ on one side and terms with $u$ on the other side. $\newline$ $4u + 3u + 8v - 2v = -3u + 3u + 2v - 2v$ $\newline$ $7u + 6v = 0$
Isolate terms with $v$ and $u$ : 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 $v$ is the output of the function $h$ for the input $u$ , we can write $h(u) = v$ . $\newline$ Therefore, $h(u) = -\frac{7}{6}u$