For a given input value q, the function g outputs a value r to satisfy the following equation. -7q+12 r=3q-4r Write a formula for g(q) in terms of q. g(q)=

Combine like terms: Combine like terms by moving all terms involving q to one side of the equation and all terms involving r to the other side. -7q + 12r = 3q - 4r Add 7q to both sides and add 4r to both sides to get: -7q + 7q + 12r + 4r = 3q + 7q - 4r + 4r Simplify to get: 16r = 10qSolve for r in terms of q: Solve for r in terms of q by dividing both sides of the equation by 16. 16r / 16 = 10q / 16 Simplify to get: r = (10/16)q Reduce the fraction (10/16) to its simplest form. r = (5/8)qWrite the function g(q): Write the function g(q) in terms of q using the relationship found in Step 2. g(q) = (5/8)q

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

-7q+12 r=3q-4r
Write a formula for
g(q) in terms of
q.

g(q)=

For a given input value $q$ , the function $g$ outputs a value $r$ to satisfy the following equation. $\newline$ $-7q + 12r = 3q - 4r$ $\newline$ Write a formula for $g(q)$ in terms of $q$ . $\newline$ $g(q) =$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

q

, the function

g

outputs a value

r

to satisfy the following equation.

\newline

-7q + 12r = 3q - 4r

\newline

Write a formula for

g(q)

in terms of

q

\newline

g(q) =

Combine like terms: Combine like terms by moving all terms involving $q$ to one side of the equation and all terms involving $r$ to the other side. $\newline$ $-7q + 12r = 3q - 4r$ $\newline$ Add $7q$ to both sides and add $4r$ to both sides to get: $\newline$ $-7q + 7q + 12r + 4r = 3q + 7q - 4r + 4r$ $\newline$ Simplify to get: $\newline$ $16r = 10q$
Solve for r in terms of q: Solve for r in terms of q by dividing both sides of the equation by $16$ . $\newline$ $\frac{16r}{16} = \frac{10q}{16}$ $\newline$ Simplify to get: $\newline$ $r = \left(\frac{10}{16}\right)q$ $\newline$ Reduce the fraction $\left(\frac{10}{16}\right)$ to its simplest form. $\newline$ $r = \left(\frac{5}{8}\right)q$
Write the function $g(q)$ : Write the function $g(q)$ in terms of $q$ using the relationship found in Step $2$ . $\newline$ $g(q) = \frac{5}{8}q$