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

-3a+6b=a+4b
Write a formula for
f(a) in terms of
a.

f(a)=◻

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

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Write equations of cosine functions using properties

Full solution

Q. For a given input value

a

, the function

f

outputs a value

b

to satisfy the following equation.

\newline

-3a+6b=a+4b

\newline

Write a formula for

f(a)

in terms of

a

.

\newline

f(a)=\square

Isolate $b$ on one side: To solve for $b$ in terms of $a$ , we need to isolate $b$ on one side of the equation. Let's start by moving all terms involving $b$ to one side and all terms involving $a$ to the other side. $\newline$ $-3a + 6b - 4b = a$
Combine like terms: Combine like terms to simplify the equation. $-3a + 2b = a$
Move term involving $a$ : Now, move the term involving $a$ on the left side to the right side by adding $3$ a to both sides of the equation. $\newline$ $2$ b = a + $3$ a
Combine terms involving $a$ : Combine the terms on the right side to get a single term involving $a$ . $\newline$ $2$ b = $4$ a
Divide both sides: Divide both sides by $2$ to solve for $b$ . $\newline$ $b = \frac{4a}{2}$
Simplify the formula: Simplify the right side to get the final formula for $b$ in terms of $a$ . $\newline$ $b = 2a$

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