For a given input value r, the function g outputs a value q to satisfy the following equation. 10 q-3r=14 Write a formula for g(r) in terms of r. g(r)=

Isolate q in equation: Isolate q in the equation 10q - 3r = 14. To do this, we will add 3r to both sides of the equation to get 10q on one side. 10q - 3r + 3r = 14 + 3r This simplifies to: 10q = 14 + 3rDivide both sides by 10: Divide both sides of the equation by 10 to solve for q. 10q / 10 = (14 + 3r) / 10 This simplifies to: q = (14 + 3r) / 10Write function g(r) in terms of r: Write the function g(r) in terms of r using the expression for q. Since q is the output of the function g for the input r, we can write: g(r) = (14 + 3r) / 10

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For a given input value
r, the function
g outputs a value
q to satisfy the following equation.

10 q-3r=14
Write a formula for
g(r) in terms of
r.

g(r)=

For a given input value $r$ , the function $g$ outputs a value $q$ to satisfy the following equation. $\newline$ $10q - 3r = 14$ $\newline$ Write a formula for $g(r)$ in terms of $r$ . $\newline$ $g(r) =$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

r

, the function

g

outputs a value

q

to satisfy the following equation.

\newline

10q - 3r = 14

\newline

Write a formula for

g(r)

in terms of

r

\newline

g(r) =

Isolate q in equation: Isolate q in the equation $10q - 3r = 14$ . $\newline$ To do this, we will add $3r$ to both sides of the equation to get $10q$ on one side. $\newline$ $10q - 3r + 3r = 14 + 3r$ $\newline$ This simplifies to: $\newline$ $10q = 14 + 3r$
Divide both sides by $10$ : Divide both sides of the equation by $10$ to solve for q. $\newline$ $\frac{10q}{10} = \frac{14 + 3r}{10}$ $\newline$ This simplifies to: $\newline$ $q = \frac{14 + 3r}{10}$
Write function $g(r)$ in terms of $r$ : Write the function $g(r)$ in terms of $r$ using the expression for $q$ . $\newline$ Since $q$ is the output of the function $g$ for the input $r$ , we can write: $\newline$ $g(r) = \frac{$ $14$ + $3$ r}{ $10$ }