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

11 q-4=3r-6
Write a formula for
f(q) in terms of
q.

f(q)=

◻

For a given input value $q$ , the function $f$ outputs a value $r$ to satisfy the following equation. $\newline$ $11 q-4=3 r-6$ $\newline$ Write a formula for $f(q)$ in terms of $q$ . $\newline$ $f(q)=\square$ $\newline$

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Power rule with rational exponents

Full solution

Q. For a given input value

q

, the function

f

outputs a value

r

to satisfy the following equation.

\newline

11 q-4=3 r-6

\newline

Write a formula for

f(q)

in terms of

q

.

\newline

f(q)=\square

\newline

Isolate r term: We are given the equation $11q - 4 = 3r - 6$ , and we need to solve for $r$ in terms of $q$ to find the function $f(q)$ . First, we will isolate the term with $r$ on one side of the equation. Add $6$ to both sides of the equation to move the constant term from the right side to the left side. $11q - 4 + 6 = 3r - 6 + 6$
Simplify left side: Now, simplify the left side of the equation by combining like terms. $11q + 2 = 3r$
Divide by $3$ : Next, we will divide both sides of the equation by $3$ to solve for $r$ . $\frac{11q + 2}{3} = r$
Write function $f(q)$ : We have now expressed $r$ in terms of $q$ . Since $f(q)$ outputs $r$ , we can write the function $f(q)$ as follows: $\newline$ $f(q) = \frac{11q + 2}{3}$

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