For a given input value u, the function g outputs a value v to satisfy the following equation. -12 u+3=8v+1 Write a formula for g(u) in terms of u. g(u)=

Write equation: Write down the given equation. The given equation is -12u + 3 = 8v + 1.Isolate v term: Isolate the term with v on one side of the equation. To do this, we subtract 1 from both sides of the equation to get -12u + 2 = 8v.Divide by 8: Divide both sides of the equation by 8 to solve for v. Doing this, we get (-12u + 2) / 8 = v.Simplify equation: Simplify the equation. We can simplify the fraction by dividing both the numerator terms by 8. This gives us (-12/8)u + (2/8) = v.Further simplify coefficients: Further simplify the coefficients in the equation. -12/8 simplifies to -3/2, and 2/8 simplifies to 1/4. So, we have (-3/2)u + 1/4 = v.Write function g(u): Write the function g(u) in terms of u. Since v is the output of the function g when the input is u, we can write g(u) = (-3/2)u + 1/4.

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

-12 u+3=8v+1
Write a formula for
g(u) in terms of
u.

g(u)=

For a given input value $u$ , the function $g$ outputs a value $v$ to satisfy the following equation. $\newline$ $-12u + 3 = 8v + 1$ $\newline$ Write a formula for $g(u)$ in terms of $u$ . $\newline$ $g(u) =$

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Math Problems

Algebra 1

Find the inverse of a linear function

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Q. For a given input value

u

, the function

g

outputs a value

v

to satisfy the following equation.

\newline

-12u + 3 = 8v + 1

\newline

Write a formula for

g(u)

in terms of

u

\newline

g(u) =

Write equation: Write down the given equation. $\newline$ The given equation is $-12u + 3 = 8v + 1$ .
Isolate $v$ term: Isolate the term with $v$ on one side of the equation. $\newline$ To do this, we subtract $1$ from both sides of the equation to get $-12$ u + $2$ = $8$ v.
Divide by $8$ : Divide both sides of the equation by $8$ to solve for $v$ . $\newline$ Doing this, we get $\frac{{-12u + 2}}{{8}} = v$ .
Simplify equation: Simplify the equation. $\newline$ We can simplify the fraction by dividing both the numerator terms by $8$ . This gives us $\frac{-12}{8}u + \frac{2}{8} = v$ .
Further simplify coefficients: Further simplify the coefficients in the equation. $\newline$ $-\frac{12}{8}$ simplifies to $-\frac{3}{2}$ , and $\frac{2}{8}$ simplifies to $\frac{1}{4}$ . So, we have $(-\frac{3}{2})u + \frac{1}{4} = v$ .
Write function $g(u)$ : Write the function $g(u)$ in terms of $u$ . $\newline$ Since $v$ is the output of the function $g$ when the input is $u$ , we can write $g(u) = \left(-\frac{3}{2}\right)u + \frac{1}{4}$ .